Math 274 - Quantum Groups
Fall, 2004

Time and place: MWF 3-4pm, 7 Evans Hall

Course control number: 55158

Professor: Mark Haiman
Office: 771 Evans
Office hours: Tues 1-3pm
Phone: (510) 642-4318


  1. Review of classical reductive algebraic groups and Lie groups, and their Lie algebras.
  2. Universal enveloping algebras.
  3. Kac-Moody algebras and their integrable representations.
  4. Quantum sl2.
  5. Quantized Kac-Moody algebras; Drinfeld's and Lusztig's formulations.
  6. Littlemann paths.
  7. Crystal bases (Kashiwara) and canonical bases (Lusztig).
  8. Geometric construction of canonical bases.
  9. Structure of (quantum) affine algebras and their representations.
  10. Conjectures and open problems.

Prerequisites: Good general algebra background.

Recommended reading:

Homework: Here are some exercises to try:

Homework will not be graded as such, but you may hand in any solutions that you would like me to comment on (no promises on how long I will take to do so).
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