Math 284: Canonical Bases in Representation Theory, Spring 2017

TTh 1-2.30pm, Science Center 411

Instructor: George Melvin

gmelvin@math.harvard.edu

Office Hours: Th 3-4pm



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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