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Math 843 |
Spring 1994 |
Lecturer: Arun Ram, University of Wisconsin, Madison
Time and Location: Lecture MWF 8:50am
Prerequisite: None
Textbook: None
Description
I. What are quantum groups
- Lie bialgebras
- Quantizations
- Existence and uniqueness of quantizations of Kac-Moody Lie algebras
II. Structure of quantum groups
- PBW-bases
- R-matrices
- Complete reducibility
- Verma modules and irreducible modules
III. Crystal bases
- Existence of the crystal base
- Crystal graphs
- Tensor products
IV.
- Specialization at q=1
- Link invariants
We will not assume any prerequisites except basic linear algebra and the definitions of rings and modules.