Algebra Seminar: Romanova -- A Kazhdan-Lusztig algorithm for Whittaker modules

Anna Romanova (University of Utah)

Friday 1 December, 12-1pm, Place: Carslaw 375

Title: A Kazhdan-Lusztig algorithm for Whittaker modules

Abstract: The category of Whittaker modules for a complex semisimple Lie
algebra generalizes the category of highest weight modules and displays
similar structural properties. In particular, Whittaker modules have
finite length composition series and all irreducible Whittaker modules
appear as quotients of certain standard Whittaker modules which are
generalizations of Verma modules. Using the localization theory of
Beilinson-Bernstein, one obtains a beautiful geometric description of
Whittaker modules as twisted sheaves of D-modules on the associated flag
variety. I use this geometric setting to develop an analogue of the
Kazhdan-Lusztig algorithm for computing the multiplicities of irreducible
Whittaker modules in the composition series of standard Whittaker modules.