Representations Of Affine Hecke Algebras
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Representations Of Affine Hecke Algebras
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Author : Nanhua Xi
language : en
Publisher: Springer
Release Date : 2006-11-15
Representations Of Affine Hecke Algebras written by Nanhua Xi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest
Representations Of Affine Hecke Algebras
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Author : N. Xi
language : en
Publisher:
Release Date : 1993
Representations Of Affine Hecke Algebras written by N. Xi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Representations Of Hecke Algebras At Roots Of Unity
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Author : Meinolf Geck
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-18
Representations Of Hecke Algebras At Roots Of Unity written by Meinolf Geck 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 2011-05-18 with Mathematics categories.
The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.
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.
Iwahori Hecke Algebras And Their Representation Theory
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Author : Ivan Cherednik
language : en
Publisher: Springer
Release Date : 2003-07-03
Iwahori Hecke Algebras And Their Representation Theory written by Ivan Cherednik and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-03 with Mathematics categories.
Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type. This volume consists of notes of the courses on Iwahori-Hecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy.
Double Affine Hecke Algebras And Congruence Groups
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Author : BOGDAN. SAHI ION (SIDDHARTHA.)
language : en
Publisher:
Release Date : 2020
Double Affine Hecke Algebras And Congruence Groups written by BOGDAN. SAHI ION (SIDDHARTHA.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Hecke Algebras With Unequal Parameters
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Author : George Lusztig
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Hecke Algebras With Unequal Parameters written by George Lusztig 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 2003 with Hecke algebras categories.
Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over $p$-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties. In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives researchers and graduate students working in the theory of algebraic groups and their representations an invaluable insight and a wealth of new and useful information.
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.
Lie Groups Geometry And Representation Theory
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Author : Victor G. Kac
language : en
Publisher: Springer
Release Date : 2018-12-12
Lie Groups Geometry And Representation Theory written by Victor G. Kac and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Mathematics categories.
This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre)
Representation Theory Of Algebraic Groups And Quantum Groups
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Author : Akihiko Gyoja
language : en
Publisher:
Release Date : 2011-03-30
Representation Theory Of Algebraic Groups And Quantum Groups written by Akihiko Gyoja and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-30 with categories.