Fiches de cours

Quantum groups and crystal bases

MATH-617

Lecturer(s) :

Gerber Thomas

Language:

English

Frequency

Only this year

Remarque

From 8 April 2019 to 31 May 2019

Summary

Quantum groups are deformations of universal enveloping algebras of certain Lie algebras. In this course, we study representation theory of these quantum groups and introduce Kashiwara's theory of crystal bases.

Content

- Kac-Moody algebras and associated quantum groups

- integrable representations

- crystal bases and crystal graphs

- example of sl(2,C)

Note

The students will be required to independently work out examples and fill in details left as exercises.

Keywords

representation theory, combinatorics, Lie algebras, quantum groups, crystals

Learning Prerequisites

Required courses

Representation theory

Learning Outcomes

By the end of the course, the student must be able to:

Resources

Bibliography

Jin Hong and Seok-Jin Kang: "Introduction to Quantum Groups and Crystal Bases" Masaki Kashiwara: "Bases cristallines des groupes quantiques" (rédigé par Charles Cochet) Daniel Bump and Anne Schilling: "Crystal Bases: Representations and Combinatorics"

In the programs

    • Semester
    • Exam form
       Oral presentation
    • Credits
      1
    • Subject examined
      Quantum groups and crystal bases
    • Lecture
      14 Hour(s)
    • Practical work
      14 Hour(s)

Reference week

 
      Lecture
      Exercise, TP
      Project, other

legend

  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German