Week 1
- January 24: course overview.
- January 26: Steinberg's tensor product theorem and some preliminary results on tensor product multiplicities; relation between TPM and subspaces of weight spaces; g-partition space and polytopes.
- Berenstein-Zelevinsky, Tensor product multiplicities and convex polytopes in partition space
Week 2
- January 31: GLn branching rules and Gelfand-Tsetlin bases; Gelfand-Tsetlin patterns; good bases and good parameterisations, after Gelfand-Zelevinsky.
- Gelfand-Zelevinsky, Multiplicities and proper bases for gln
- February 2: quantised universal enveloping algebras; structure of U_q(sl2) and its representation theory.
- Jantzen, Lectures on quantum groups
- Hong-Kang, Introduction to quantum groups and crystal bases
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