Algebra och geometri: Bigrassmannian permutations and Verma modules

  • Datum: –17.00
  • Plats: Zoom Meeting https://uu-se.zoom.us/j/64555726999 Meeting ID: 645 5572 6999 For passcode, please contact: Volodymyr.Mazorchuk@math.uu.se
  • Föreläsare: Rafael Mrden
  • Arrangör: Matematiska institutionen
  • Kontaktperson: 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
Mazorchuk.