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Affine Hecke Algebras and Orthogonal Polynomials
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  • Cited by 37
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Braverman, Alexander Kazhdan, David and Patnaik, Manish M. 2016. Iwahori–Hecke algebras for p-adic loop groups. Inventiones mathematicae, Vol. 204, Issue. 2, p. 347.


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    Elliot, Ross and Gukov, Sergei 2016. Exceptional knot homology. Journal of Knot Theory and Its Ramifications, Vol. 25, Issue. 03, p. 1640003.


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    Motegi, Kohei 2015. Nonstandard Representations of Type C Affine Hecke Algebra from K-Operators. Letters in Mathematical Physics, Vol. 105, Issue. 8, p. 1165.


    van Diejen, J. F. and Emsiz, E. 2015. Integrable Boundary Interactions for Ruijsenaars’ Difference Toda Chain. Communications in Mathematical Physics, Vol. 337, Issue. 1, p. 171.


    Cameron, Stephen and Vinroot, C. Ryan 2014. A product formula for multivariate Rogers–Szegő polynomials. The Ramanujan Journal, Vol. 35, Issue. 3, p. 479.


    Parkinson, James 2014. On calibrated representations and the Plancherel Theorem for affine Hecke algebras. Journal of Algebraic Combinatorics, Vol. 40, Issue. 2, p. 331.


    Stokman, Jasper 2014. The c-function expansion of a basic hypergeometric function associated to root systems. Annals of Mathematics, Vol. 179, Issue. 1, p. 253.


    van Diejen, J. F. and Emsiz, E. 2014. Orthogonality of Macdonald polynomials with unitary parameters. Mathematische Zeitschrift, Vol. 276, Issue. 1-2, p. 517.


    Bliem, Thomas and Kousidis, Stavros 2013. The number of flags in finite vector spaces: asymptotic normality and Mahonian statistics. Journal of Algebraic Combinatorics, Vol. 37, Issue. 2, p. 361.


    Cherednik, Ivan and Ma, Xiaoguang 2013. Spherical and Whittaker functions via DAHA I. Selecta Mathematica, Vol. 19, Issue. 3, p. 737.


    Lenart, Cristian and Schilling, Anne 2013. Crystal energy functions via the charge in types A and C. Mathematische Zeitschrift, Vol. 273, Issue. 1-2, p. 401.


    Masuda, Yasuho 2013. Kernel identities for van Diejen’s q-difference operators and transformation formulas for multiple basic hypergeometric series. The Ramanujan Journal, Vol. 32, Issue. 2, p. 281.


    Mekareeya, Noppadol Song, Jaewon and Tachikawa, Yuji 2013. 2d TQFT structure of the superconformal indices with outer-automorphism twists. Journal of High Energy Physics, Vol. 2013, Issue. 3,


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    Affine Hecke Algebras and Orthogonal Polynomials
    • Online ISBN: 9780511542824
    • Book DOI: https://doi.org/10.1017/CBO9780511542824
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Book description

In recent years there has developed a satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters. These polynomials include as special cases: symmetric functions; zonal spherical functions on real and p-adic reductive Lie groups; the Jacobi polynomials of Heckman and Opdam; and the Askey–Wilson polynomials, which themselves include as special or limiting cases all the classical families of orthogonal polynomials in one variable. This book, first published in 2003, is a comprehensive and organised account of the subject aims to provide a unified foundation for this theory, to which the author has been a principal contributor. It is an essentially self-contained treatment, accessible to graduate students familiar with root systems and Weyl groups. The first four chapters are preparatory to Chapter V, which is the heart of the book and contains all the main results in full generality.

Reviews

‘This is a beautiful book, treating in a concise and clear way the recent developments concerning the connection between orthogonal polynomials in several variables and root systems in two or more parameters.’

Source: Zentralblatt für Mathematik

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.


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