Lie groups and quantum groups

Instructor: Vera Serganova
Email address: serganov@math
  • webpage:http://math.berkeley.edu/~serganov
  • Phone Number: 642-2150
  • Office hours: M 4:00-5:30, W 11:00-12:30 in 709 Evans
  • Topics
  • Weyl character formula
  • Verma modules and category O
  • Harish-Chandra theorem
  • Cohomology of Lie algebras
  • Representations of GL(n): Schur-Weyl duality and Gelfand-Tsetlin basis
  • Flag varieties, Bruhat decomposition
  • Borel-Weil-Bott theorem
  • Nilpotent cone and Kostant theorem
  • Beilinson-Bernstein localization
  • Hopf algebras
  • Quantum groups
  • Canonical bases
  • Real Lie groups and symmetric spaces(if time permits)
  • Infinite-dimensional Lie algebras (if time permits)
  • Recommended Texts:Fulton-Harris: Representation theory (a first course), Lusztig: Introduction to quantum groups, Chari-Pressley: A guide to quantum groups, Dixmier: Enveloping algebras, Jantzen: Representations of algebraic groups, Kac: Infinite-dimensional Lie algebras, Humphreys: Representations of semisimple Lie algebras in BGG category O.
  • Problem sets
  • Problem set 1
  • Problem set 2
  • Problem set 3
  • Problem set 4
  • Problem set 5
  • Problem set 6