An Overview of Kirillov-Reshtikhin Modules and Crystals

Abstract: Kirillov-Reshetikhin (KR) modules are an important class of finite dimensional representations associated to an affine Lie algebra and the associated Yangian and quantum group. KR modules are known to appear in many integrable systems and govern the dynamics. In this talk, we will give an overview of the role KR modules play in the category of finite dimensional representations, R-matrices and the fusion construction, their (conjectural) crystal bases, and how they relate to Demazure modules. In particular, we will focus on how to construct their crystal bases combinatorially and the different types of character theories. As time permits, we will discuss some of the relations with (quantum) integrable systems.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.