Algebra and geometry: Kostant's problem and a monoidal action of projective functors

  • Date: –17:00
  • Location: Zoom meeting
  • Lecturer: Hankyung Ko (Uppsala)
  • Organiser: Matematiska institutionen
  • Contact person: Volodymyr Mazorchuk
  • Seminarium

Let g be a semisimple complex Lie algebra and let M be a g-module. Consider A(M), the space of linear endomorphisms on M on which the adjoint action of g is locally finite. A classical question of Kostant

is: when is the canonical map from U(g) to A(M) surjective? I will reformulate this problem using the language of monoidal categories. If M is a simple highest weight module, then the answer to the problem is equivalent to a certain category equivalence, determined by decomposing the action of projective functors on M. This leads to a conjectural complete answer to Kostant's problem for simple highest weight modules in terms of Kazhdan-Lusztig combinatorics.

 This is a joint work with Walter Mazorchuk and Rafael Mrden.