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Workshop on Hecke Algebras and Lie Theory

赫克代数和李理论研讨会

基本信息

批准号：
1623501
负责人：
Siddhartha Sahi
金额：
$ 1.6万
依托单位：
Rutgers University New Brunswick
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2016
资助国家：
美国
起止时间：
2016-04-01 至 2018-03-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1623501&HistoricalAwards=false
关键词：
Workshop Hecke Algebras Lie Theory

项目摘要

This award supports US-based participants, primarily graduate students and postdoctoral researchers, in the "Workshop on Hecke Algebras and Lie Theory," held May 12-15, 2016 at the University of Ottawa. The workshop brings together experts in algebraic combinatorics and Lie theory with the goal of fostering the international collaboration between researchers in several areas connected to representation theory and algebraic combinatorics, including Lie superalgebras, extended affine Lie algebras, and Hecke algebras. In addition to talks by experts in the field, the workshop includes a mini-course accessible to non-experts, including junior researchers, that covers recent progress in double affine Hecke algebras and related areas. Hecke algebras of finite and affine Weyl groups arise naturally as convolution algebras associated to finite and locally compact groups, and they play a prominent role in the representation theory of finite groups of Lie type and of reductive p-adic groups. In the early 1990's a class of algebras, known as double affine Hecke algebras, was introduced in connection with affine quantum Knizhnik-Zamolodchikov equations. Since then, profound connections have been discovered between double affine Hecke algebras and a broad spectrum of areas in mathematics, including combinatorics, algebraic geometry, number theory, representation theory, harmonic analysis, knot theory, special functions, many body problems, and conformal field theory. Recent results hint at a new and promising connection between double affine Hecke algebras and Lie superalgebras and open the door to many intriguing possibilities that will be explored at the workshop. The website for the workshop is https://www.fields.utoronto.ca/programs/scientific/15-16/Hecke/

该奖项支持美国的参与者，主要是研究生和博士后研究人员，在“Hecke代数和李理论研讨会”，2016年5月12日至15日在渥太华大学举行。该研讨会汇集了代数组合学和李理论的专家，旨在促进与表示论和代数组合学相关的几个领域的研究人员之间的国际合作，包括李超代数，扩展仿射李代数和Hecke代数。除了该领域专家的会谈外，研讨会还包括一个小型课程，可供非专家（包括初级研究人员）使用，涵盖了双仿射Hecke代数及相关领域的最新进展。有限和仿射Weyl群的Hecke代数自然地作为与有限和局部紧群相关的卷积代数出现，它们在李型有限群和约化p进群的表示论中发挥了突出的作用。在20世纪90年代早期，一类代数，称为双仿射Hecke代数，被引入与仿射量子Knizhnik-Zamolodchikov方程。从那时起，深刻的联系已被发现之间的双重仿射赫克代数和广泛的领域在数学，包括组合学，代数几何，数论，表示论，调和分析，纽结理论，特殊功能，许多机构的问题，和共形场论。最近的结果暗示了双仿射Hecke代数和李超代数之间新的和有前途的联系，并为研讨会上将探索的许多有趣的可能性打开了大门。研讨会的网址是https://www.fields.utoronto.ca/programs/scientific/15-16/Hecke/