Program
Schur-Weyl duality
Student No.:70
Time:Fri 16:30-17:30, Sep.14
Instructor:Yuval Flicker  
Place:Lecture Hall, Jin Chun Yuan West Bldg.
Starting Date:2018-9-14
Ending Date:2018-9-14

Abstract:
A duality theorem in mathematics relates two seemingly unrelated objects: this is its attraction. An early example was discovered by Schur in his 1901 thesis. He found a relation between representations of the symmetric group S_d, and those of GL(n). A super analogue, reminiscent of bosons and fermions, involving the supergroup GL(m|n), followed. In influential works of 1986, Drinfeld and Jimbo extended Schur’s duality to relate representations of the quantum general linear group, with those of the Hecke algebra, the latter defined using their universal R-matrices solutions of the Yang-Baxter equations. Chari and Pressley then studied the affine case. I shall attempt to describe the ultimate extension, to the super affine quantum situation. In particular I construct a functor relating suitable categories of affine Hecke modules - important in number theory - and of affine quantum supergroups - from physics, as a modern twist of Schur's duality, afforded by Yamane's presentation of these supergroups.


About Professor Yuval Flicker:
Yuval Flicker is an American mathematician. His primary research interests include Automorphic and Admissible Representations, Automorphic forms over function fields, Arithmetic Geometry, and so on. He received his PhD degree from the University of Cambridge in 1978, in the area of transcendental number theory. His thesis advisor was Alan Baker. He taught at Princeton, Columbia, Harvard, Ohio State, and Ariel University, where he is now a Professor.


摘要:
数学中的对偶定理能将两个本不相关的对象联系起来:令人着迷。一个早先的例子是由Schur在他1901年的博士论文里发现。他发现了对称群S_d和一般线性群GL(n)的表示之间的联系。接着又有在超群上类似的结果,所涉及的是超群GL(m|n),让人想到波色子和费米子。Drinfeld和Jimbo在他们1986年有影响力的工作中将Schur的对偶性扩展到联系量子一般线性群和Hecke代数的表示之间的联系,后者是通过它们Yang-Baxter方程万有R-矩阵解来定义。Chari和Pressley接着研究仿射情形。我将尝试去描述最终的扩展,即超仿射量子情形。特别地,我通过Yamane关于超群的描述构造了一个函子,联系了有关仿射Hecke模和仿射量子超群的相关范畴,作为Schur的对偶性的一个现代转变。


主讲人简介:
Yuval Flicker是一位美国数学家。他的主要研究方向包括:自守表示和可容许表示,函数域上的自守形式以及算术几何等方面。1978年,他获得了剑桥大学的博士学位。他的论文导师是超越数理论方面的Alan Baker。Flicker教授曾执教于普林斯顿大学、哥伦比亚大学、哈佛大学和俄亥俄州立大学,现就职于阿里尔大学。