Syllabus 280: Quantum Groups and Crystal Bases
Winter 2006

Lectures: TTh 9:00-10:20am, MSB 3106, Small Seminar Room
Instructor: Anne Schilling, MSB 3222, phone: 754-9371,
Text: There are several books on quantum groups and crystal bases. Some of the material will be based on the following books:
  • Introduction to Quantum Groups and Crystal Bases by J. Hong and S.-J. Kang, AMS GSM 42
  • A Guide to Quantum Groups by V. Chari and A. Pressley, Cambridge
  • Lectures on Quantum Groups by J. C. Jantzen, AMS GSM 6
  • Representations of Quantum Algebras and Combinatorics of Young Tableaux by S. Ariki, AMS ULECT 26
  • Quantum Groups and Their Primitive Ideals by A. Joseph, Springer Verlag
  • Quantum Groups by C. Kassel, Springer Verlag
We will also use recent papers which I will hand out or announce in class.
Grading: Every registered student is required to present a paper in class. A list of suitable papers and topics will be discussed in class.

Course description

Quantum groups were first introduced independently by Drinfeld and Jimbo in the study of statistical mechanical models and have since appeared in many areas of mathematics and physics, such as representation theory, the theory of knots and links and topological quantum field theory. In this class we will see how quantum groups arose in physics and study their representation theory, in particular crystal bases. Some familiarity with Lie algebras is desirable, but not strictly necessary. Topics will include: