Affine Hecke Algebras And Orthogonal Polynomials

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Affine Hecke Algebras And Orthogonal Polynomials

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Author : I. G. Macdonald
language : en
Publisher: Cambridge University Press
Release Date : 2003-03-20

Affine Hecke Algebras And Orthogonal Polynomials written by I. G. Macdonald and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-20 with Mathematics categories.

First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.

Affine Hecke Algebras And Orthogonal Polynomials

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Author : I. G. Macdonald
language : en
Publisher: Cambridge University Press
Release Date : 2003-03-20

Affine Hecke Algebras And Orthogonal Polynomials written by I. G. Macdonald and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-20 with Mathematics categories.

A satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters, has developed in recent years. This comprehensive account of the subject provides a unified foundation for the theory to which I.G. Macdonald has been a principal contributor. The first four chapters lead up to Chapter 5 which contains all the main results.

Laredo Lectures On Orthogonal Polynomials And Special Functions

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Author : Renato Alvarez-Nodarse
language : en
Publisher: Nova Publishers
Release Date : 2004

Laredo Lectures On Orthogonal Polynomials And Special Functions written by Renato Alvarez-Nodarse and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This new book presents research in orthogonal polynomials and special functions. Recent developments in the theory and accomplishments of the last decade are pointed out and directions for research in the future are identified. The topics covered include matrix orthogonal polynomials, spectral theory and special functions, Asymptotics for orthogonal polynomials via Riemann-Hilbert methods, Polynomial wavelets and Koornwinder polynomials.

Double Affine Hecke Algebras And Congruence Groups

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Author : Bogdan Ion
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18

Double Affine Hecke Algebras And Congruence Groups written by Bogdan Ion and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Education categories.

The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data. We show that DAAG/DAHA always admit a faithful action by auto-morphisms of a finite index subgroup of the Artin group of type A2, which descends to a faithful outer action of a congruence subgroup of SL(2, Z)or PSL(2, Z). This was previously known only in some special cases and, to the best of our knowledge, not even conjectured to hold in full generality. It turns out that the structural intricacies of DAAG/DAHA are captured by the underlying semisimple data and, to a large extent, even by adjoint data; we prove our main result by reduction to the adjoint case. Adjoint DAAG/DAHA correspond in a natural way to affine Lie algebras, or more precisely to their affinized Weyl groups, which are the semi-direct products W 􀀁 Q∨ of the Weyl group W with the coroot lattice Q∨. They were defined topologically by van der Lek, and independently, algebraically, by Cherednik. We now describe our results for the adjoint case in greater detail. We first give a new Coxeter-type presentation for adjoint DAAG as quotients of the Coxeter braid groups associated to certain crystallographic diagrams that we call double affine Coxeter diagrams. As a consequence we show that the rank two Artin groups of type A2,B2,G2 act by automorphisms on the adjoint DAAG/DAHA associated to affine Lie algebras of twist number r =1, 2, 3, respec-tively. This extends a fundamental result of Cherednik for r =1. We show further that the above rank two Artin group action descends to an outer action of the congruence subgroup Γ1(r). In particular, Γ1(r) acts naturally on the set of isomorphism classes of representations of an adjoint DAAG/DAHA of twist number r, giving rise to a projective representation of Γ1(r)on the spaceof aΓ1(r)-stable representation. We also provide a classification of the involutions of Kazhdan-Lusztig type that appear in the context of these actions.

Double Affine Hecke Algebras

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Author : Ivan Cherednik
language : en
Publisher: Cambridge University Press
Release Date : 2005-03-21

Double Affine Hecke Algebras written by Ivan Cherednik and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-21 with Mathematics categories.

This is an essentially self-contained monograph centered on the new double Hecke algebra technique.

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Author :
language : en
Publisher: World Scientific
Release Date :

written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Representation Theory Of Algebraic Groups And Quantum Groups

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Author : Akihiko Gyoja
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-25

Representation Theory Of Algebraic Groups And Quantum Groups written by Akihiko Gyoja and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-25 with Mathematics categories.

Invited articles by top notch experts Focus is on topics in representation theory of algebraic groups and quantum groups Of interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics

Surveys In Combinatorics 2003

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Author : C. D. Wensley
language : en
Publisher: Cambridge University Press
Release Date : 2003-07-24

Surveys In Combinatorics 2003 written by C. D. Wensley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-24 with Mathematics categories.

The British Combinatorial Conference is held every two years and is a key event for mathematicians worldwide working in combinatorics. In June 2003 the conference was held at the University of Wales, Bangor. The papers contained here are surveys contributed by the invited speakers and are of the high quality that befits the event. There is also a tribute to Bill Tutte who had a long-standing association with the BCC. The papers cover topics currently attracting significant research interest as well as some less traditional areas such as the combinatorics of protecting digital content. They will form an excellent resource for established researchers as well as graduate students who will find much here to inspire future work.

Q Series From A Contemporary Perspective

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Author : Mourad Ismail
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Q Series From A Contemporary Perspective written by Mourad Ismail and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

This volume presents the proceedings of the Summer Research Conference on q-series and related topics held at Mount Holyoke College (Hadley, Massachusetts). All of the papers were contributed by participants and offer original research. Articles in the book reflect the diversity of areas that overlap with q-series, as well as the usefulness of q-series across the mathematical sciences. The conference was held in honour of Richard Askey on the occasion of his 65th birthday.

Classical Hypergeometric Functions And Generalizations

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Author : Howard S. Cohl
language : en
Publisher: American Mathematical Society
Release Date : 2025-04-23

Classical Hypergeometric Functions And Generalizations written by Howard S. Cohl and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-23 with Mathematics categories.

This is the first volume of a two-volume collection of recent research results related to hypergeometric functions. The second volume (Contemporary Mathematics, Volume 819) is titled Applications and $q$-Extensions of Hypergeometric Functions. This volume contains the proceedings of a minisymposium and two AMS special sessions in three conferences: Minisymposium on All Things Hypergeometric, $q$-series and Generalizations at the 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA-16), June 13–17, 2022, Centre de Recherches Mathématiques, Montréal, Québec, Canada; AMS Special Session on Hypergeometric Functions and $q$-series at the 2022 AMS Fall Western Sectional Meeting, October 22–23, 2022, University of Utah, Salt Lake City, Utah; and the AMS Special Session on Hypergeometric Functions, $q$-series and Generalizations, at the 2023 AMS Spring Eastern Virtual Sectional Meeting, April 1–2, 2023. This book provides a sampling of current mathematical research related to the Gauss hypergeometric function, and as well, its immediate generalizations and extensions. This includes the generalized hypergeometric functions that originated with Kummer, as well as such classical special functions as Lamé and Heun functions. It also includes certain functions relevant to algebraic geometry, such as hypergeometric functions over finite fields. All research articles come with extensive bibliographies and can serve as entry points to the current literature.