Algebra and geometry: Bigrassmannian permutations and Verma modules

  • Date: –17:00
  • Location: Zoom Meeting Meeting ID: 645 5572 6999 For passcode, please contact:
  • Lecturer: Rafael Mrden
  • Organiser: Matematiska institutionen
  • Contact person: Volodymyr Mazorchuk
  • Seminarium

We describe an unexpected connection between bigrassmannian permutations and
the socle of quotients of
Verma modules in type A. As a consequence, we show that the socular
constituents in the cokernel of the
inclusion of a Verma module indexed by a permutation w into the dominant Verma
module are determined by
the essential set of w (in the sense of Fulton), and their degrees in the
graded picture are determined by
the associated rank function. Another application is a formula for the first
extension from a simple
module to a Verma module. This is a joint work with Hankyung Ko and Volodymyr