Program
Quantum Groups and Crystal Bases
Student No.:50
Time:Wed/Thu 18:00-19:50, 2015-03-04~ 2015-06-18 (except for public holidays)
Instructor:Xiaoguang Ma  [Tsinghua University]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2015-3-4
Ending Date:2015-6-18

 

 

Description:

 

Quantum groups were introduced by Drinfeld and Jimbo independently. They are a family of Hopf algebras that are certain deformation of universal enveloping algebras of Kac-Moody algebras. Lusztig introduced the canonical bases in order to study the representation theory of quantum groups. Crystal bases are a kind of limit version of the canonical bases. The theory of crystal bases were developed by Kashiwara and many others. In this course will provide an introductory of these theories. 

 

 

Prerequisite:

 

Basic knowledge of Lie algebras and Lie groups.

 

 

Reference:

 

V. Chari and A. Pressley, A Guide to Quantum Groups

V. G. Drinfeld, Quantum Groups

W. Fulton and J. Harris, Representation Theory: a first course

M. Kashiwara, On Crystal Bases of the q-analogue of Universal Enveloping Algebras

G. Lusztig, Canonical Bases arising from Quantized Enveloping Algebras

J. Hong and S-J. Kang, Introduction to Quantu