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Sunday, May 10, 2020 | History

12 edition of Double Affine Hecke Algebras found in the catalog.

Double Affine Hecke Algebras

by Ivan Cherednik

  • 396 Want to read
  • 34 Currently reading

Published by Cambridge University Press .
Written in English

    Subjects:
  • Linear algebra,
  • Orthogonal polynomials,
  • Hecke algebras,
  • Mathematics,
  • Science/Mathematics,
  • Algebra - General,
  • Mathematics / Algebra / General,
  • Harmonic analysis,
  • Affine algebraic groups,
  • Knizhnik-Zamoldchikov equation

  • Edition Notes

    London Mathematical Society Lecture Note Series

    The Physical Object
    FormatPaperback
    Number of Pages446
    ID Numbers
    Open LibraryOL7748395M
    ISBN 100521609186
    ISBN 109780521609180

    Abstract. The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group : Bogdan Ion, Siddhartha Sahi. I. CherednikLectures on Knizhnik–Zamolodchikov equations and Hecke algebras Quantum Many-Body Problems and Representation Theory, MSJ Memoirs (), pp. Google ScholarCited by: 6.

    The number of simple modules of the Hecke algebras of type G(r,1,n) is not the double coset basis when $\cysHr$ is the Hecke algebra of a Coxeter group, but coincides with the double coset. A skein theoretic model for the double affine Hecke algebras University of Liverpool More recently Peter and I had a look at the models of the double affine Hecke algebras by Burella et al, and came up with a variant of these based this time on braids in the thickened torus.

    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' () "characteristic-free'' approach to the representation. Pages from Volume (), Issue 1 by Ivan Cherednik.


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Double Affine Hecke Algebras by Ivan Cherednik Download PDF EPUB FB2

Book Description This is an essentially self-contained monograph in an intriguing field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics. It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications.5/5(1).

Buy Double Affine Hecke Algebras (London Mathematical Society Lecture Note Series) on FREE SHIPPING on qualified orders Double Affine Hecke Algebras (London Mathematical Society Lecture Note Series): Ivan Cherednik: : BooksCited by: This is a unique, essentially self-contained, monograph in a new field of fundamental importance for representation theory, harmonic analysis, mathematical physics, and combinatorics.

Double Affine Hecke Algebras book is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications. Double affine Hecke algebra Ivan Cherednik This is a unique, essentially self-contained, monograph in a new field of fundamental importance for representation theory, harmonic analysis, mathematical physics, and combinatorics.

Double Affine Hecke Algebras DOWNLOAD HERE This is a unique, essentially self-contained monograph centered on the new double Hecke algebra is an essentially self-contained monograph. It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications.

Chapter 1 is devoted to the Knizhnik-Zamolodchikov equations attached to root systems and their relations to affine Hecke algebras, Kac-Moody algebras, and Fourier analysis. In mathematics, a double affine Hecke algebra, or Cherednik algebra, is an algebra containing the Hecke algebra of an affine Weyl group, given as the quotient of the group ring of a double affine braid group.

They were introduced by Cherednik, who used them to prove Macdonald's constant term conjecture for Macdonald polynomials. Abstract: This paper is based on the introduction to the monograph ``Double affine Hecke algebras'' to be published by Cambridge University Press.

The connections with Knizhnik-Zamolodchikov equations, Kac-Moody algebras, tau-function, harmonic analysis Cited by: 8.

LECTURE 1: REMINDER ON AFFINE HECKE ALGEBRAS SETH SHELLEY-ABRAHAMSON Abstract. These are notes for a seminar talk at the MIT-Northeastern Spring Double A ne Hecke Algebras and Elliptic Hall Algebras (DAHAEHA) Seminar.

Contents 1. Goals 1 2. Review of Coxeter Groups and Their Hecke Algebras 1 Coxeter Groups 2 Braid Groups 3 Rational Double affine Hecke algebras (RDAHA for short) have been intro-duced by Etingof and Ginzburg in They are associative algebras associated with a complex reflection group W and a parameter c.

Their rep-resentation theory is similar to the representation theory of semi-simple Lie algebras. 2 The Double Affine Hecke Algebra The extended affine Weyl group. Let N ≥ 2 and let D = D N be the affine Dynkin diagram of affine type (the cyclic graph with N vertices if N ≥ 3).

The N vertices are labeled by the numbers 0, 1,N − 1 (anticlockwise if N ≥ 3). We identify occasionally the set of labels by the group of integers Cited by: Introduction to Double Hecke algebras Ivan Cherednik1,2 February 1, This paper is based on the introduction to the monograph ”Double affine Hecke algebras” to be published by Cambridge University Press.

It is based on a series of lectures delivered by the author in Kyoto (–), at Uni. The role of quantum groups is taken over by Hecke algebras.

The book under review provides an extensive introduction to Cherednik’s theory and to its numerous applications. Quantum Yang-Baxter equation. @MISC{_doubleaffine, author = {}, title = {Double affine Hecke algebras, by Ivan Cherednik, London Mathematical Society,}, year = {}} Share.

Ivan Cherednik introduced generalizations of affine Hecke algebras, the so-called double affine Hecke algebra (usually referred to as DAHA). Using this he was able to give a proof of Macdonald's constant term conjecture for Macdonald polynomials (building on work of Eric Opdam).

Modified Cherednik algebra 52 Orbifold Hecke algebras 52 Hecke algebras attached to Fuchsian groups 53 Hecke algebras of wallpaper groups and del Pezzo surfaces 55 The Knizhnik-Zamolodchikov functor 55 Proof of Theorem 56 Example: the simplest case of double affine Hecke algebras 57 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. Affine flag manifolds are infinite dimensional versions of familiar objects such as Graßmann varieties. The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid - explaining the significance of these and related objects (such as double affine Hecke algebras and affine Springer fibers) in representation theory (e.g., the theory Brand: Birkhäuser Basel.

This includes the affine quantum Schur–Weyl reciprocity, the bridging role of affine q-Schur algebras between representations of the quantum loop algebras and those of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel–Hall algebra with a proof of the Cited by: This section provides the schedule of lecture topics for the course and a complete set of lecture notes prepared jointly by Prof.

Pavel Etingof and Xiaoguang Ma. Mathematics» Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics Rational Cherednik algebras and Hecke algebras for. The main aim of the paper is to formulate and prove a result about the structure of double affine Hecke algebras which allows its two commutative subalgebras to play a symmetric role.

LECTURE 2: DOUBLE AFFINE HECKE ALGEBRAS JOSE SIMENTAL Abstract. These are notes for a talk given at the MIT-Northeastern Graduate Student Seminar on Double A ne Hecke Algebras and Elliptic Hall Algebras, Spring Contents 1.

Goals and structure of the talk 1 2. Double A ne Hecke Algebras 2 Reminders 2 Double a ne Hecke algebras 3 Double affine Hecke algebras. [Ivan Cherednik] -- This book is a unique, essentially self-contained, monograph in a new field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics.Affine flag manifolds are infinite dimensional versions of familiar objects such as Graßmann varieties.

The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid - explaining the significance of these and related objects (such as double affine Hecke algebras and affine Springer fibers) in representation theory (e.g., the theory.