A Kazhdan--Lusztig algorithm for Whittaker modules
Whittaker modules are certain representations of Lie algebras which were first studied by Kostant for their relationship to the Whittaker equation in number theory. From a representation-theoretic viewpoint, Whittaker modules are interesting in their own right, as infinite-dimensional representations with enough imposed structure to make them tractable to study. Milicic and Soergel placed Kostant’s Whittaker modules in a larger category N, and McDowell showed that all irreducible objects in N appear as quotients of certain standard Whittaker modules, which generalize Verma modules. There is also a geometric incarnation of the category N in terms of twisted D-modules on the associated flag variety. Using this geometric description, one can develop an algorithm for computing composition multiplicities of standard Whittaker modules. In this talk, I’ll describe the parallel algebraic and geometric worlds which contribute to this story, then sketch the algorithm which answers the multiplicity question in category N.
Dr Anna Romanov, University of Sydney