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Double Hecke Algebras and Applications

Double Hecke Algebras and Applications
双赫克代数及其应用
批准号:
0200276
负责人:
Ivan Cherednik
金额:
$11.15万
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
2002
资助国家:
美国
项目状态:
已结题
起止时间:
2002-05-01 至 2006-04-30

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中文摘要
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英文摘要
The purpose of this project is to study double affine Hecke algebras (DAHA), as previously introduced by the principal investigator. They have proved to be very useful in representation theory, the theory of special and spherical functions, conformal field theory, and combinatorics. The main objectives include: (1) A general classification of the semisimple, spherical, unitary, and Fourier-univariant representations of DAHA; (2) the classification of finite dimensional representations of DAHA for generic q, with applications to Macdonald's eta-type identities, Kac-Moody characters, and degenerate Bessel functions; (3) the theory of representations of DAHA at roots of unity, connections with the monodromy of the double affine KZ equations and elliptic braid groups; (4) classificaton of the Fourier-invariant uitary representations of DAHA with applications to Gauss-Selberg sums and Verlinde algebras; (5) harmonic analysis on semisimple representations of DAHA in the compact and noncompact cases, at roots of unity, and in the elliptic case.This is a project in the area of mathematics known as Representation Theory. The nature of representation theory, and what makes it so useful in so many areas of mathematics and science, is that it is a way of studying and encoding symmetries, whereever they may occur, in nature or abstractly. The purpose of this project is to study and develop the properties of a new representation-theoretic tool, "double affine Hecke algebras," that can be used in the application of representation theory to physics (conformal field theory) and combinatorics. Combinatorics is the science of counting the possible arrangements and ways of organizing collections of anything (e.g., atoms, pebbles, star clusters).
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Double Affine Hecke Algebras
Double Affine Hecke Algebras
DOUBLE AFFINE HECKE ALGEBRAS
Double Affine Hecke Algebras
国内基金
海外基金
Hecke特征值的Linnik问题及识别问题
  • 批准号:
    12271458
  • 项目类别:
    面上项目
  • 资助金额:
    45万元
  • 批准年份:
    2022
  • 负责人:
    刘旭金
  • 依托单位:
Mock theta函数与Hecke型级数
  • 批准号:
    12171375
  • 项目类别:
    面上项目
  • 资助金额:
    50万元
  • 批准年份:
    2021
  • 负责人:
    王六权
  • 依托单位:
Hecke-Rogers类型恒等式及其截断性质的研究
  • 批准号:
    12001376
  • 项目类别:
    青年科学基金项目
  • 资助金额:
    24.0万元
  • 批准年份:
    2020
  • 负责人:
    王春
  • 依托单位:
与对合相关的Hecke代数中的若干问题
  • 批准号:
    11901030
  • 项目类别:
    青年科学基金项目
  • 资助金额:
    28.9万元
  • 批准年份:
    2019
  • 负责人:
    孙玉姣
  • 依托单位: