Academic literature on the topic 'Ariki-Koike algebras'
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Journal articles on the topic "Ariki-Koike algebras"
Jacon, Nicolas, and Cédric Lecouvey. "Cores of Ariki-Koike algebras." Documenta Mathematica 26 (2021): 103–24. http://dx.doi.org/10.4171/dm/810.
Full textHalverson, Tom, and Arun Ram. "Murnaghan-Nakayama Rules for Characters of Iwahori-Hecke Algebras of the Complex Reflection Groups G(r, p, n)." Canadian Journal of Mathematics 50, no. 1 (February 1, 1998): 167–92. http://dx.doi.org/10.4153/cjm-1998-009-x.
Full textDu, Jie, and Hebing Rui. "SPECHT MODULES FOR ARIKI-KOIKE ALGEBRAS." Communications in Algebra 29, no. 10 (August 31, 2001): 4701–19. http://dx.doi.org/10.1081/agb-100106782.
Full textRostam, Salim. "Stuttering blocks of Ariki–Koike algebras." Algebraic Combinatorics 2, no. 1 (2019): 75–118. http://dx.doi.org/10.5802/alco.40.
Full textDu, Jie, and Hebing Rui. "Ariki-Koike algebras with semisimple bottoms." Mathematische Zeitschrift 234, no. 4 (August 1, 2000): 807–30. http://dx.doi.org/10.1007/s002090050009.
Full textDipper, Richard, and Andrew Mathas. "Morita equivalences of Ariki-Koike algebras." Mathematische Zeitschrift 240, no. 3 (July 1, 2002): 579–610. http://dx.doi.org/10.1007/s002090100371.
Full textFayers, Matthew. "Core blocks of Ariki–Koike algebras." Journal of Algebraic Combinatorics 26, no. 1 (January 10, 2007): 47–81. http://dx.doi.org/10.1007/s10801-006-0048-x.
Full textYang, Guiyu. "Nil-Coxeter algebras and nil-Ariki-Koike algebras." Frontiers of Mathematics in China 10, no. 6 (September 21, 2015): 1473–81. http://dx.doi.org/10.1007/s11464-015-0498-3.
Full textSakamoto, Masahiro, and Toshiaki Shoji. "Schur–Weyl Reciprocity for Ariki–Koike Algebras." Journal of Algebra 221, no. 1 (November 1999): 293–314. http://dx.doi.org/10.1006/jabr.1999.7973.
Full textSawada, Nobuharu, and Toshiaki Shoji. "Modified Ariki-Koike algebras and cyclotomic q-Schur algebras." Mathematische Zeitschrift 249, no. 4 (January 7, 2005): 829–67. http://dx.doi.org/10.1007/s00209-004-0739-8.
Full textDissertations / Theses on the topic "Ariki-Koike algebras"
Stoll, Friederike. "On the action of Ariki-Koike algebras on tensor space." [S.l. : s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB12168104.
Full textYu, Shona Huimin. "The Cyclotomic Birman-Murakami-Wenzl Algebras." Thesis, The University of Sydney, 2007. http://hdl.handle.net/2123/3560.
Full textYu, Shona Huimin. "The Cyclotomic Birman-Murakami-Wenzl Algebras." School of Mathematics and Statistics, 2007. http://hdl.handle.net/2123/3560.
Full textThis thesis presents a study of the cyclotomic BMW algebras, introduced by Haring-Oldenburg as a generalization of the BMW (Birman-Murakami-Wenzl) algebras related to the cyclotomic Hecke algebras of type G(k,1,n) (also known as Ariki-Koike algebras) and type B knot theory involving affine/cylindrical tangles. The motivation behind the definition of the BMW algebras may be traced back to an important problem in knot theory; namely, that of classifying knots (and links) up to isotopy. The algebraic definition of the BMW algebras uses generators and relations originally inspired by the Kauffman link invariant. They are intimately connected with the Artin braid group of type A, Iwahori-Hecke algebras of type A, and with many diagram algebras, such as the Brauer and Temperley-Lieb algebras. Geometrically, the BMW algebra is isomorphic to the Kauffman Tangle algebra. The representations and the cellularity of the BMW algebra have now been extensively studied in the literature. These algebras also feature in the theory of quantum groups, statistical mechanics, and topological quantum field theory. In view of these relationships between the BMW algebras and several objects of "type A", several authors have since naturally generalized the BMW algberas for other types of Artin groups. Motivated by knot theory associated with the Artin braid group of type B, Haring-Oldenburg introduced the cyclotomic BMW algebras B_n^k as a generalization of the BMW algebras such that the Ariki-Koike algebra h_{n,k} is a quotient of B_n^k, in the same way the Iwahori-Hecke algebra of type A is a quotient of the BMW algebra. In this thesis, we investigate the structure of these algebras and show they have a topological realization as a certain cylindrical analogue of the Kauffman Tangle algebra. In particular, they are shown to be R-free of rank k^n (2n-1)!! and bases that may be explicitly described both algebraically and diagrammatically in terms of cylindrical tangles are obtained. Unlike the BMW and Ariki-Koike algebras, one must impose extra so-called "admissibility conditions" on the parameters of the ground ring in order for these results to hold. This is due to potential torsion caused by the polynomial relation of order k imposed on one of the generators of B_n^k. It turns out that the representation theory of B_2^k is crucial in determining these conditions precisely. The representation theory of B_2^k is analysed in detail in a joint preprint with Wilcox in [45] (http://arxiv.org/abs/math/0611518). The admissibility conditions and a universal ground ring with admissible parameters are given explicitly in Chapter 3. The admissibility conditions are also closely related to the existence of a non-degenerate Markov trace function of B_n^k which is then used together with the cyclotomic Brauer algebras in the linear independency arguments contained in Chapter 4. Furthermore, in Chapter 5, we prove the cyclotomic BMW algebras are cellular, in the sense of Graham and Lehrer. The proof uses the cellularity of the Ariki-Koike algebras (Graham-Lehrer [16] and Dipper-James-Mathas [8]) and an appropriate "lifting" of a cellular basis of the Ariki-Koike algebras into B_n^k, which is compatible with a certain anti-involution of B_n^k. When k = 1, the results in this thesis specialize to those previously established for the BMW algebras by Morton-Wasserman [30], Enyang [9], and Xi [47]. REMARKS: During the writing of this thesis, Goodman and Hauschild-Mosley also attempt similar arguments to establish the freeness and diagram algebra results mentioned above. However, they withdrew their preprints ([14] and [15]), due to issues with their generic ground ring crucial to their linear independence arguments. A similar strategy to that proposed in [14], together with different trace maps and the study of rings with admissible parameters in Chapter 3, is used in establishing linear independency of our basis in Chapter 4. Since the submission of this thesis, new versions of these preprints have been released in which Goodman and Hauschild-Mosley use alternative topological and Jones basic construction theory type arguments to establish freeness of B_n^k and an isomorphism with the cyclotomic Kauffman Tangle algebra. However, they require their ground rings to be an integral domain with parameters satisfying the (slightly stronger) admissibility conditions introduced by Wilcox and the author in [45]. Also, under these conditions, Goodman has obtained cellularity results. Rui and Xu have also obtained freeness and cellularity results when k is odd, and later Rui and Si for general k, under the assumption that \delta is invertible and using another stronger condition called "u-admissibility". The methods and arguments employed are strongly influenced by those used by Ariki, Mathas and Rui [3] for the cyclotomic Nazarov-Wenzl algebras and involve the construction of seminormal representations; their preprints have recently been released on the arXiv. It should also be noted there are slight differences between the definitions of cyclotomic BMW algebras and ground rings used, as explained partly above. Furthermore, Goodman and Rui-Si-Xu use a weaker definition of cellularity, to bypass a problem discovered in their original proofs relating to the anti-involution axiom of the original Graham-Lehrer definition. This Ph.D. thesis, completed at the University of Sydney, was submitted September 2007 and passed December 2007.
Rostam, Salim. "Algèbres de Hecke carquois et généralisations d'algèbres d'Iwahori-Hecke." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLV063/document.
Full textThis thesis is devoted to the study of quiver Hecke algebras and some generalisations of Iwahori-Hecke algebras. We begin with two results concerning quiver Hecke algebras, first when the quiver has several connected components and second when the quiver has an automorphism of finite order. We then recall an isomorphism of Brundan-Kleshchev and Rouquier between Ariki-Koike algebras and certain cyclotomic quiver Hecke algebras. From this, on the one hand we deduce that a well-known important Morita equivalence between Ariki--Koike algebras comes from an isomorphism, on the other hand we give a cyclotomic quiver Hecke-like presentation for the Hecke algebra of type G(r,p,n). We also generalise the isomorphism of Brundan-Kleshchev to prove that cyclotomic Yokonuma-Hecke algebras are particular cases of cyclotomic quiver Hecke algebras. Finally, we study a problem of algebraic combinatorics, related to the representation theory of Ariki-Koike algebras. Using the abacus representation of partitions and solving, via an existence theorem for binary matrices, a constrained optimisation problem with integer variables, we prove that a stuttering multiset of residues necessarily comes from a stuttering multipartition
Corlett, Kelvin. "On homomorphisms between Specht modules for the Ariki-Koike algebra." Thesis, University of East Anglia, 2012. https://ueaeprints.uea.ac.uk/47289/.
Full textGerber, Thomas. "Matrices de décomposition des algèbres d'Ariki-Koike et isomorphismes de cristaux dans les espaces de Fock." Phd thesis, Université François Rabelais - Tours, 2014. http://tel.archives-ouvertes.fr/tel-01057480.
Full textStoll, Friederike [Verfasser]. "On the action of Ariki-Koike algebras on tensor space / vorgelegt von Friederike Stoll." 2005. http://d-nb.info/976745917/34.
Full textBook chapters on the topic "Ariki-Koike algebras"
Geck, Meinolf, and Nicolas Jacon. "Representation Theory of Ariki–Koike Algebras." In Representations of Hecke Algebras at Roots of Unity, 261–307. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-716-7_5.
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