Introduction to Coxeter groups and Iwahori-Hecke algebras.
Speaker(s): Xiang Fu(BICMR)
Time: March 16 - March 30, 2024
Venue: 82J12, Jiayibing Building, Jingchunyuan 82, BICMR
Abstract：
The Iwahori-Hecke algebras are deformations of the groups algebras of Coxeter groups. Since the advent of the Kazhdan-Lusztig theory of Iwahori-Hecke algebras, the study of such algebras has occupied a prominent position within the disciplines of representation theory and algebraic geometry. These seminars aim to provide a basic introduction to Iwahori-Hecke algebras, starting from an excursion in basic Coxeter group theory progressing towards an overview of some of the most exciting current developments in the Kazhdan-Lusztig theory.
The introduction on Coxeter groups includes: Tits representation, root systems, exchange/deletion condition, Bruhat ordering, and a number of (equivalent) characterizations when groups generated by involutions are Coxeter groups, including the existence of a cocycle function. Time permitting the classification theory of Coxeter groups may be presented.
The introduction on Iwahori-Hecke algebras will cover an overview of Iwahori-Hecke algebras and the Kazhdan-Lusztig theory, covering the basics and a survey on current research developments on Kazhdan-Lusztig theory, including an introduction on Williamson’s work. Time permitting a presentation on the existence of a cellular-algebra structure in the Iwahori-Hecke algebras may be given.
Speakers：
Xiang Fu（BICMR)
Hongsheng Hu（BICMR)
Gaston Burrull (BICMR)
Time：
March 16, 23, 30
1:30-3:00 p.m. 3:30-5:00 p.m.
