Workshop on Hecke Algebras and Lie Theory

该奖项为 2016 年 5 月 12 日至 15 日在渥太华大学举行的“赫克代数和李理论研讨会”中的美国参与者（主要是研究生和博士后研究人员）提供支持。该研讨会汇集了代数组合学和李理论方面的专家，旨在促进与表示论和代数组合学相关的多个领域的研究人员之间的国际合作，包括李超代数、扩展仿射李代数和赫克代数。除了该领域专家的演讲之外，研讨会还包括一门可供非专家（包括初级研究人员）使用的迷你课程，涵盖了双仿射赫克代数和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，并且它们在 Lie 型有限群和还原 p 进群的表示论中发挥着重要作用。 20 世纪 90 年代初，一类代数（称为双仿射 Hecke 代数）与仿射量子 Knizhnik-Zamolodchikov 方程相关被引入。从那时起，人们发现了双仿射赫克代数与广泛的数学领域之间的深刻联系，包括组合数学、代数几何、数论、表示论、调和分析、结论、特殊函数、许多体问题和共形场论。最近的结果暗示了双仿射赫克代数和李超代数之间存在新的、有希望的联系，并为研讨会上将探讨的许多有趣的可能性打开了大门。研讨会的网站是 https://www.fields.utoronto.ca/programs/scientific/15-16/Hecke/

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/