Lecture Series on Representation Theory

 

Lecture Series 1

 

Title: Semi-infinite Lakshmibai-Seshadri paths and level-zero extremal weight modules over quantum affine algebras

 

Lecturer: Satoshi Naito (Institute of Science Tokyo)

 

Abstract: In this lecture. I first define semi-infinite Lakshmibai-Seshadri (LS) paths, which are analogs of ordinary LS paths, defined by using the semi-infinite Bruhat order in place  of the ordinary Bruhat order on an affine Weyl group. Then, I give the precise relation between semi-infinite LS paths and what we call level-zero LS paths. Finally, I will explain how these semi-infinite LS paths provide a realization of the crystal bases of level-zero extremal weight modules over quantum affine algebras.

 

Place:  129동 309호 (SNU)

Lecture 1. 06.08 (Mon) 10:00~11:30

Lecture 2. 06.09 (Tue) 10:00~11:30

Lecture 3. 06.10 (Wed) 10:00~11:30

Lecture 4. 06.11 (Thu) 10:00~11:30

 

Lecture Series 2

Title: Schubert varieties, Lusztig varieties, and Hessenberg varieties
 

Lecturer: Jaehyun Hong (IBS, 복소기하연구단)

Abstract: Let $G$ be a simple algebraic group and $B$ be a Borel subgroup of $G$.  Hessenberg varieties are subvarieties of the flag variety $G/B$ parametrized by elements in the Lie algebra of $G$. The monodromy action on the cohomology of regular semisimple Hessenberg varieties factors through the Weyl group, and various problems in combinatorics and representation theory can be transformed into problems in geometry and topology. Examples include chromatic quasisymmetric functions of the unit interval graphs. Lusztig varieties are subvarieties of the flag variety $G/B$ parametrized by elements in $G$, introduced in 1985 by Lusztig to develop a representation theory of reductive groups, especially of finite groups of Lie type. Their origins differ, but recent progress shows that, in the context of the character theory of the Hecke algebra, they play a similar role. The goal of this lecture series is to understand their relationship.

 

Place:  129동 309호 (SNU)
Lecture 1. 06.08 (Mon) 15:00~16:30 Hessenberg varieties 

Lecture 2. 06.10 (Wed) 15:00~16:30 Lusztig varieties

Lecture 3. 06.11 (Thu) 15:00~16:30 Weyl group representations