Relevant bibliographies by topics / Hecke algebras

Academic literature on the topic 'Hecke algebras'

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Published: 4 June 2021
Last updated: 11 March 2023

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Journal articles on the topic "Hecke algebras"

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Rouquier, Raphaël. "Quiver Hecke Algebras and 2-Lie Algebras." Algebra Colloquium 19, no. 02 (May 3, 2012): 359–410. http://dx.doi.org/10.1142/s1005386712000247.

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We provide an introduction to the 2-representation theory of Kac-Moody algebras, starting with basic properties of nil Hecke algebras and quiver Hecke algebras, and continuing with the resulting monoidal categories, which have a geometric description via quiver varieties, in certain cases. We present basic properties of 2-representations and describe simple 2-representations, via cyclotomic quiver Hecke algebras, and through microlocalized quiver varieties.
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Yang, Guiyu, and Yanbo Li. "Standardly based algebras and 0-Hecke algebras." Journal of Algebra and Its Applications 14, no. 10 (September 2015): 1550141. http://dx.doi.org/10.1142/s0219498815501418.

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In this paper we prove that standardly based algebras are invariant under Morita equivalences. As an application, we prove 0-Hecke algebras and 0-Schur algebras are standardly based algebras. From this point of view, we give a new way to construct the simple modules of 0-Hecke algebras, and prove that the dimension of the center of a symmetric 0-Hecke algebra is not less than the number of its simple modules.
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Krieg, Aloys. "Hecke algebras." Memoirs of the American Mathematical Society 87, no. 435 (1990): 0. http://dx.doi.org/10.1090/memo/0435.

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Takebayashi, Tadayoshi. "Double affine Hecke algebras and elliptic Hecke algebras." Journal of Algebra 253, no. 2 (July 2002): 314–49. http://dx.doi.org/10.1016/s0021-8693(02)00055-8.

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Savage, Alistair. "Affine Wreath Product Algebras." International Mathematics Research Notices 2020, no. 10 (May 24, 2018): 2977–3041. http://dx.doi.org/10.1093/imrn/rny092.

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Abstract We study the structure and representation theory of affine wreath product algebras and their cyclotomic quotients. These algebras, which appear naturally in Heisenberg categorification, simultaneously unify and generalize many important algebras appearing in the literature. In particular, special cases include degenerate affine Hecke algebras, affine Sergeev algebras (degenerate affine Hecke–Clifford algebras), and wreath Hecke algebras. In some cases, specializing the results of the current paper recovers known results, but with unified and simplified proofs. In other cases, we obtain new results, including proofs of two open conjectures of Kleshchev and Muth.
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Liu, Wille. "Knizhnik–Zamolodchikov functor for degenerate double affine Hecke algebras: algebraic theory." Representation Theory of the American Mathematical Society 26, no. 30 (August 30, 2022): 906–61. http://dx.doi.org/10.1090/ert/614.

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In this article, we define an algebraic version of the Knizhnik–Zamolodchikov (KZ) functor for the degenerate double affine Hecke algebras (a.k.a. trigonometric Cherednik algebras). We compare it with the KZ monodromy functor constructed by Varagnolo–Vasserot. We prove the double centraliser property for our functor and give a characterisation of its kernel. We establish these results for a family of algebras, called quiver double Hecke algebras, which includes the degenerate double affine Hecke algebras as special cases.
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Opdam, Eric, and Maarten Solleveld. "Homological algebra for affine Hecke algebras." Advances in Mathematics 220, no. 5 (March 2009): 1549–601. http://dx.doi.org/10.1016/j.aim.2008.11.002.

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Rostam, Salim. "Cyclotomic Yokonuma–Hecke algebras are cyclotomic quiver Hecke algebras." Advances in Mathematics 311 (April 2017): 662–729. http://dx.doi.org/10.1016/j.aim.2017.03.004.

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Poulain d'Andecy, L., and R. Walker. "Affine Hecke algebras and generalizations of quiver Hecke algebras of type B." Proceedings of the Edinburgh Mathematical Society 63, no. 2 (March 9, 2020): 531–78. http://dx.doi.org/10.1017/s0013091519000294.

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AbstractWe define and study cyclotomic quotients of affine Hecke algebras of type B. We establish an isomorphism between direct sums of blocks of these algebras and a generalization, for type B, of cyclotomic quiver Hecke algebras, which are a family of graded algebras closely related to algebras introduced by Varagnolo and Vasserot. Inspired by the work of Brundan and Kleshchev, we first give a family of isomorphisms for the corresponding result in type A which includes their original isomorphism. We then select a particular isomorphism from this family and use it to prove our result.
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Putcha, Mohan S. "Monoid Hecke algebras." Transactions of the American Mathematical Society 349, no. 9 (1997): 3517–34. http://dx.doi.org/10.1090/s0002-9947-97-01823-0.

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Dissertations / Theses on the topic "Hecke algebras"

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Uhl, Christine. "Quantum Drinfeld Hecke Algebras." Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc862764/.

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Quantum Drinfeld Hecke algebras extend both Lusztig's graded Hecke algebras and the symplectic reflection algebras of Etingof and Ginzburg to the quantum setting. A quantum (or skew) polynomial ring is generated by variables which commute only up to a set of quantum parameters. Certain finite groups may act by graded automorphisms on a quantum polynomial ring and quantum Drinfeld Hecke algebras deform the natural semi-direct product. We classify these algebras for the infinite family of complex reflection groups acting in arbitrary dimension. We also classify quantum Drinfeld Hecke algebras in arbitrary dimension for the infinite family of mystic reflection groups of Kirkman, Kuzmanovich, and Zhang, who showed they satisfy a Shephard-Todd-Chevalley theorem in the quantum setting. Using a classification of automorphisms of quantum polynomial rings in low dimension, we develop tools for studying quantum Drinfeld Hecke algebras in 3 dimensions. We describe the parameter space of such algebras using special properties of the quantum determinant in low dimension; although the quantum determinant is not a homomorphism in general, it is a homomorphism on the finite linear groups acting in dimension 3.
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Parkinson, James William. "Buildings and Hecke Algebras." Thesis, The University of Sydney, 2005. http://hdl.handle.net/2123/642.

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We establish a strong connection between buildings and Hecke algebras through the study of two algebras of averaging operators on buildings. To each locally finite regular building we associate a natural algebra B of chamber set averaging operators, and when the building is affine we also define an algebra A of vertex set averaging operators. In the affine case, it is shown how the building gives rise to a combinatorial and geometric description of the Macdonald spherical functions, and of the centers of affine Hecke algebras. The algebra homomorphisms from A into the complex numbers are studied, and some associated spherical harmonic analysis is conducted. This generalises known results concerning spherical functions on groups of p-adic type. As an application of this spherical harmonic analysis we prove a local limit theorem for radial random walks on affine buildings.
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Parkinson, James William. "Buildings and Hecke Algebras." University of Sydney. Mathematics and Statistics, 2005. http://hdl.handle.net/2123/642.

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We establish a strong connection between buildings and Hecke algebras through the study of two algebras of averaging operators on buildings. To each locally finite regular building we associate a natural algebra B of chamber set averaging operators, and when the building is affine we also define an algebra A of vertex set averaging operators. In the affine case, it is shown how the building gives rise to a combinatorial and geometric description of the Macdonald spherical functions, and of the centers of affine Hecke algebras. The algebra homomorphisms from A into the complex numbers are studied, and some associated spherical harmonic analysis is conducted. This generalises known results concerning spherical functions on groups of p-adic type. As an application of this spherical harmonic analysis we prove a local limit theorem for radial random walks on affine buildings.
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Boys, Clinton. "Alternating quiver Hecke algebras." Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/12725.

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This thesis consists of a detailed study of alternating quiver Hecke algebras, which are alternating analogues of quiver Hecke algebras as defined by Khovanov-Lauda and Rouquier. The main theorem gives an isomorphism between alternating quiver Hecke algebras and alternating Hecke algebras, as introduced by Mitsuhashi, in the style of Brundan and Kleshchev, provided the quantum characteristic is odd. A proof is obtained by adapting recent methods of Hu and Mathas, which rely on seminormal forms and coefficient systems. A presentation for alternating quiver Hecke algebras by generators and relations, reminiscent of the KLR presentation for Hecke algebras, is also given. Finally, some steps are taken towards discussing the representation theoretic consequences of the results.
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Gehles, Katrin Eva. "Properties of Cherednik algebras and graded Hecke algebras." Thesis, University of Glasgow, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.433167.

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TERRAGNI, TOMMASO. "Hecke algebras associated to coxeter groups." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2012. http://hdl.handle.net/10281/29634.

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In this thesis, we study cohomological properties of Hecke algebras $H_q(W,S)$ associated with arbitrary Coxeter groups $(W,S)$. Under mild conditions, it is possible to canonically define the Euler characteristic of such an algebra. We define an almost-canonical complex of $H$-modules that allows one to compute the Euler characteristic of $H$. It turns out that the Euler characteristic of the algebra has an interpretation as a combinatorial object attached to the Coxeter group: indeed, for suitable choices of the base ring, it is the inverse of the Poincaré series. Some other results about Coxeter groups are proved, in particular one new characterization of minimal non-spherical, non-affine types is given.
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Stoica, Emanuel (Emanuel I. ). "Unitary representations of rational Cherednik algebras and Hecke algebras." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/64606.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 49-50).
We begin the study of unitary representations in the lowest weight category of rational Cherednik algebras of complex reflection groups. We provide the complete classification of unitary representations for the symmetric group, the dihedral group, as well as some additional partial results. We also study the unitary representations of Hecke algebras of complex reflection groups and provide a complete classification in the case of the symmetric group. We conclude that the KZ functor defined in [16] preserves unitarity in type A. Finally, we formulate a few conjectures concerning the classification of unitary representations for other types and the preservation of unitarity by the KZ functor and the restriction functors defined in [2].
by Emanuel Stoica.
Ph.D.
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Heyer, Claudius. "Applications of parabolic Hecke algebras: parabolic induction and Hecke polynomials." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20137.

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Im ersten Teil wird eine neue Konstruktion der parabolischen Induktion für pro-p Iwahori-Heckemoduln gegeben. Dabei taucht eine neue Klasse von Algebren auf, die in gewisser Weise als Interpolation zwischen der pro-p Iwahori-Heckealgebra einer p-adischen reduktiven Gruppe $G$ und derjenigen einer Leviuntergruppe $M$ von $G$ gedacht werden kann. Für diese Algebren wird ein Induktionsfunktor definiert und eine Transitivitätseigenschaft bewiesen. Dies liefert einen neuen Beweis für die Transitivität der parabolischen Induktion für Moduln über der pro-p Iwahori-Heckealgebra. Ferner wird eine Funktion auf einer parabolischen Untergruppe untersucht, die als Werte nur p-Potenzen annimmt. Es wird gezeigt, dass sie eine Funktion auf der (pro-p) Iwahori-Weylgruppe von $M$ definiert, und dass die so definierte Funktion monoton steigend bzgl. der Bruhat-Ordnung ist und einen Vergleich der Längenfunktionen zwischen der Iwahori-Weylgruppe von $M$ und derjenigen der Iwahori-Weylgruppe von $G$ erlaubt. Im zweiten Teil wird ein allgemeiner Zerlegungssatz für Polynome über der sphärischen (parahorischen) Heckealgebra einer p-adischen reduktiven Gruppe $G$ bewiesen. Diese Zerlegung findet über einer parabolischen Heckealgebra statt, die die Heckealgebra von $G$ enthält. Für den Beweis des Zerlegungssatzes wird vorausgesetzt, dass die gewählte parabolische Untergruppe in einer nichtstumpfen enthalten ist. Des Weiteren werden die nichtstumpfen parabolischen Untergruppen von $G$ klassifiziert.
The first part deals with a new construction of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. This construction exhibits a new class of algebras that can be thought of as an interpolation between the pro-p Iwahori-Hecke algebra of a p-adic reductive group $G$ and the corresponding algebra of a Levi subgroup $M$ of $G$. For these algebras we define a new induction functor and prove a transitivity property. This gives a new proof of the transitivity of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. Further, a function on a parabolic subgroup with p-power values is studied. We show that it induces a function on the (pro-p) Iwahori-Weyl group of $M$, that it is monotonically increasing with respect to the Bruhat order, and that it allows to compare the length function on the Iwahori-Weyl group of $M$ with the one on the Iwahori-Weyl group of $G$. In the second part a general decomposition theorem for polynomials over the spherical (parahoric) Hecke algebra of a p-adic reductive group $G$ is proved. The proof requires that the chosen parabolic subgroup is contained in a non-obtuse one. Moreover, we give a classification of non-obtuse parabolic subgroups of $G$.
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Neshitov, Alexander. "Motivic Decompositions and Hecke-Type Algebras." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35009.

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Let G be a split semisimple algebraic group over a field k. Our main objects of interest are twisted forms of projective homogeneous G-varieties. These varieties have been important objects of research in algebraic geometry since the 1960's. The theory of Chow motives and their decompositions is a powerful tool for studying twisted forms of projective homogeneous varieties. Motivic decompositions were discussed in the works of Rost, Karpenko, Merkurjev, Chernousov, Calmes, Petrov, Semenov, Zainoulline, Gille and other researchers. The main goal of the present thesis is to connect motivic decompositions of twisted homogeneous varieties to decompositions of certain modules over Hecke-type algebras that allow purely combinatorial description. We work in a slightly more general situation than Chow motives, namely we consider the category of h-motives for an oriented cohomology theory h. Examples of h include Chow groups, Grothendieck K_0, algebraic cobordism of Levine-Morel, Morava K-theory and many other examples. For a group G there is the notion of a versal torsor such that any G-torsor over an infinite field can be obtained as a specialization of a versal torsor. We restrict our attention to the case of twisted homogeneous spaces of the form E/P where P is a special parabolic subgroup of G. The main result of this thesis states that there is a one-to-one correspondence between h-motivic decompositions of the variety E/P and direct sum decompositions of modules DFP* over the graded formal affine Demazure algebra DF. This algebra was defined by Hoffnung, Malagon-Lopez, Savage and Zainoulline combinatorially in terms of the character lattice, the Weyl group and the formal group law of the cohomology theory h. In the classical case h=CH the graded formal affine Demazure algebra DF coincides with the nil Hecke ring, introduced by Kostant and Kumar in 1986. So the Chow motivic decompositions of versal homogeneous spaces correspond to decompositions of certain modules over the nil Hecke ring. As an application, we give a purely combinatorial proof of the indecomposability of the Chow motive of generic Severi-Brauer varieties and the versal twisted form of HSpin8/P1.
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Fakiolas, A. P. "Hecke algebras and the Lusztig isomorphism." Thesis, University of Warwick, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379611.

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Books on the topic "Hecke algebras"

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Krieg, Aloys. Hecke algebras. Providence, R.I., USA: American Mathematical Society, 1990.

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Xi, Nanhua. Representations of affine Hecke algebras. Berlin: Springer-Verlag, 1994.

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Xi, Nanhua. Representations of Affine Hecke Algebras. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0074130.

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Blocks and families for cyclotomic Hecke algebras. Berlin: Springer, 2009.

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Ceccherini-Silberstein, Tullio, Fabio Scarabotti, and Filippo Tolli. Gelfand Triples and Their Hecke Algebras. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-51607-9.

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Nicolas, Jacon, and SpringerLink (Online service), eds. Representations of Hecke Algebras at Roots of Unity. London: Springer-Verlag London Limited, 2011.

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Iwahori-Hecke algebras and Schur algebras of the symmetric group. Providence, R.I: American Mathematical Society, 1999.

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Chlouveraki, Maria. Blocks and Families for Cyclotomic Hecke Algebras. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03064-2.

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Cherednik, Ivan, Yavor Markov, Roger Howe, and George Lusztig. Iwahori-Hecke Algebras and their Representation Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/b10326.

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Ivan, Cherednik, Baldoni M. Welleda 1949-, and Barbasch D. 1951-, eds. Iwahori-Hecke algebras and their representation theory: Lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, June 28-July 6, 1999. Berlin: Springer, 2002.

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Book chapters on the topic "Hecke algebras"

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Bonnafé, Cédric. "Hecke Algebras." In Algebra and Applications, 53–69. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70736-5_4.

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Bump, Daniel. "Hecke Algebras." In Lie Groups, 471–83. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8024-2_46.

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Bump, Daniel. "Hecke Algebras." In Lie Groups, 384–96. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4757-4094-3_48.

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Ceccherini-Silberstein, Tullio, Fabio Scarabotti, and Filippo Tolli. "Hecke Algebras." In Lecture Notes in Mathematics, 11–29. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-51607-9_2.

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Xi, Nanhua. "Hecke algebras." In Lecture Notes in Mathematics, 1–17. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0074131.

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Chlouveraki, Maria. "On Hecke Algebras." In Lecture Notes in Mathematics, 71–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03064-2_4.

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Ram, Arun, and Jacqui Ramagge. "Affine Hecke Algebras, Cyclotomic Hecke algebras and Clifford Theory." In A Tribute to C. S. Seshadri, 428–66. Gurgaon: Hindustan Book Agency, 2003. http://dx.doi.org/10.1007/978-93-86279-11-8_26.

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Geck, Meinolf, and Nicolas Jacon. "Generic Iwahori–Hecke Algebras." In Representations of Hecke Algebras at Roots of Unity, 1–58. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-716-7_1.

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Garrett, Paul. "Generic and Hecke Algebras." In Buildings and Classical Groups, 87–100. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5340-9_6.

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Xi, Nanhua. "Isogenous affine Hecke algebras." In Lecture Notes in Mathematics, 93–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0074139.

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Conference papers on the topic "Hecke algebras"

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Lee, Dong-il. "Basis theorem for degenerate affine Hecke algebras." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002365.

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Ariki, Susumu. "On cyclotomic quiver Hecke algebras of affine type." In The Eighth China–Japan–Korea International Symposium on Ring Theory. WORLD SCIENTIFIC, 2021. http://dx.doi.org/10.1142/9789811230295_0001.

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Wybourne, B. G., and M. Yang. "q—Deformation of symmetric functions and Hecke algebras Hn(q) of type An−1." In Group Theory in Physics: Proceedings of the international symposium held in honor of Professor Marcos Moshinsky. AIP, 1992. http://dx.doi.org/10.1063/1.42845.

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Cooperman, Gene, and Michael Tselman. "New sequential and parallel algorithms for generating high dimension Hecke algebras using the condensation technique." In the 1996 international symposium. New York, New York, USA: ACM Press, 1996. http://dx.doi.org/10.1145/236869.236927.

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Fieker, Claus, William Hart, Tommy Hofmann, and Fredrik Johansson. "Nemo/Hecke." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3087604.3087611.

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Yamane, Hiroyuki. "ON REPRESENTATION THEORIES OF IWAHORI-HECKE ALGEBRAS Hq(W) AT ROOTS q OF UNITY (IN PARTICULAR, EXPLICIT FORMULAS ON $H_{n_{\sqrt{1}}(S_{n})}$ and $H_{n-1_{\sqrt{1}}(S_{n})}$)." In The Fifth Nankai Workshop. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814503761_0010.

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Bigelow, Stephen. "Homological representations of the Iwahori–Hecke algebra." In Conference on the Topology of Manifolds of Dimensions 3 and 4. Mathematical Sciences Publishers, 2004. http://dx.doi.org/10.2140/gtm.2004.7.493.

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GÉRARDIN, PAUL, and K. F. LAI. "ASYMPTOTIC BEHAVIOR OF EIGENFUNCTIONS FOR THE HECKE ALGEBRA ON HOMOGENEOUS TREES." In Proceedings of the International Workshop. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792303_0009.

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Wysoczański, Janusz. "On a cubic Hecke algebra associated with the quantum group Uq(2)." In Noncommutative Harmonic Analysis with Applications to Probability II. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2010. http://dx.doi.org/10.4064/bc89-0-22.

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Hwang, Jun-Muk. "Hecke curves on the moduli space of vector bundles over an algebraic curve." In Proceedings of the Symposium. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705105_0005.

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