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Relevant bibliographies by topics / Macdonald spherical function

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Academic literature on the topic 'Macdonald spherical function'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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Journal articles on the topic "Macdonald spherical function"

1

Shilin, I. A., and Junesang Choi. "Some Connections between the Spherical and Parabolic Bases on the Cone Expressed in terms of the Macdonald Function." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/741079.

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Computing the matrix elements of the linear operator, which transforms the spherical basis ofSO(3,1)-representation space into the hyperbolic basis, very recently, Shilin and Choi (2013) presented an integral formula involving the product of two Legendre functions of the first kind expressed in terms of 4F3-hypergeometric function and, using the general Mehler-Fock transform, another integral formula for the Legendre function of the first kind. In the sequel, we investigate the pairwise connections between the spherical, hyperbolic, and parabolic bases. Using the above connections, we give an interesting series involving the Gauss hypergeometric functions expressed in terms of the Macdonald function.

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Fratila, Dragos. "Cusp eigenforms and the hall algebra of an elliptic curve." Compositio Mathematica 149, no. 6 (March 4, 2013): 914–58. http://dx.doi.org/10.1112/s0010437x12000784.

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AbstractWe give an explicit construction of the cusp eigenforms on an elliptic curve defined over a finite field, using the theory of Hall algebras and the Langlands correspondence for function fields and ${\mathrm{GL} }_{n} $. As a consequence we obtain a description of the Hall algebra of an elliptic curve as an infinite tensor product of simpler algebras. We prove that all these algebras are specializations of a universal spherical Hall algebra (as defined and studied by Burban and Schiffmann [On the Hall algebra of an elliptic curve I, Preprint (2005), arXiv:math/0505148 [math.AG]] and Schiffmann and Vasserot [The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials, Compositio Math. 147 (2011), 188–234]).

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Letzter, Gail. "Quantum zonal spherical functions and Macdonald polynomials." Advances in Mathematics 189, no. 1 (December 2004): 88–147. http://dx.doi.org/10.1016/j.aim.2003.11.007.

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Mantero, A. M., and A. Zappa. "Macdonald formula for spherical functions on affine buildings." Annales de la faculté des sciences de Toulouse Mathématiques 20, no. 4 (2011): 669–758. http://dx.doi.org/10.5802/afst.1321.

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5

oblomkov, alexei a., and jasper v. stokman. "vector valued spherical functions and macdonald–koornwinder polynomials." Compositio Mathematica 141, no. 05 (September 2005): 1310–50. http://dx.doi.org/10.1112/s0010437x05001636.

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van Diejen, J. F., and E. Emsiz. "Pieri formulas for Macdonald’s spherical functions and polynomials." Mathematische Zeitschrift 269, no. 1-2 (May 30, 2010): 281–92. http://dx.doi.org/10.1007/s00209-010-0727-0.

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van Diejen, J. F., E. Emsiz, and I. N. Zurrián. "Affine Pieri rule for periodic Macdonald spherical functions and fusion rings." Advances in Mathematics 392 (December 2021): 108027. http://dx.doi.org/10.1016/j.aim.2021.108027.

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8

van Diejen, J. F., and E. Emsiz. "Unitary representations of affine Hecke algebras related to Macdonald spherical functions." Journal of Algebra 354, no. 1 (March 2012): 180–210. http://dx.doi.org/10.1016/j.jalgebra.2012.01.005.

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Schiffmann, O., and E. Vasserot. "The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials." Compositio Mathematica 147, no. 1 (July 7, 2010): 188–234. http://dx.doi.org/10.1112/s0010437x10004872.

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AbstractWe exhibit a strong link between the Hall algebra HX of an elliptic curve X defined over a finite field 𝔽l (or, more precisely, its spherical subalgebra U+X) and Cherednik’s double affine Hecke algebras $\ddot {\mathbf {H}}_n$ of type GLn, for all n. This allows us to obtain a geometric construction of the Macdonald polynomials Pλ(q,t−1) in terms of certain functions (Eisenstein series) on the moduli space of semistable vector bundles on the elliptic curve X.

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Noumi, Masatoshi. "Macdonald's Symmetric Polynomials as Zonal Spherical Functions on Some Quantum Homogeneous Spaces." Advances in Mathematics 123, no. 1 (October 1996): 16–77. http://dx.doi.org/10.1006/aima.1996.0066.

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Dissertations / Theses on the topic "Macdonald spherical function"

1

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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Book chapters on the topic "Macdonald spherical function"

1

Ueno, Kimio, and Tadayoshi Takebayashi. "Zonal spherical functions on quantum symmetric spaces and MacDonald's symmetric polynomials." In Lecture Notes in Mathematics, 142–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0101186.

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2

Nelsen, K., and A. Ram. "Kostka–Foulkes polynomials and Macdonald spherical functions." In Surveys in Combinatorics 2003, 325–70. Cambridge University Press, 2003. http://dx.doi.org/10.1017/cbo9781107359970.011.

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