Double Affine Hecke Algebras
Double Affine Hecke Algebras
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DOI：
10.1017/cbo9780511546501
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发表时间：
2005-04
期刊：
影响因子：
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通讯作者：
I. Cherednik
中科院分区：
文献类型：
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作者：
I. Cherednik
这是一本独特的，本质上自给自足的专著，在一个对表象理论、调和分析、数学物理和组合学具有基本重要性的新领域。它是关于双仿射Hecke代数(也称为Cherednik代数)及其令人印象深刻的应用的一般信息的主要来源。第一章讨论了根系上的Knizhnik-Zamolodchikov方程及其与仿射Hecke代数、Kac-Moody代数和傅立叶分析的关系。第二章系统地阐述了一维达哈的表象理论。这是特殊函数理论中最简单的情况，但绝不是微不足道的，有着深刻的联系。第三章是关于Daha的一般知识，包括它在Macdonald多项式、傅立叶变换、Gauss-Selberg积分、Verlinde代数和Gauss和中的应用。这本书是为数学家和物理学家、专家和学生设计的，所有那些想要掌握新的双重Hecke代数技术的人。
This is a unique, essentially self-contained, monograph in a new 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. 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. Chapter 2 contains a systematic exposition of the representation theory of the one-dimensional DAHA. It is the simplest case but far from trivial with deep connections in the theory of special functions. Chapter 3 is about DAHA in full generality, including applications to Macdonald polynomials, Fourier transforms, Gauss-Selberg integrals, Verlinde algebras, and Gaussian sums. This book is designed for mathematicians and physicists, experts and students, all those who want to master the new double Hecke algebra technique.