University of Sydney Algebra Seminar
Anna Romanov
Friday 28 October, 12-1pm, Place: Carslaw 157-257
Filtrations of Whittaker modules
Whittaker modules are a class of representations which show up naturally in various settings in representation theory. One approach to studying them is to place them in a natural ambient category and examine the structural properties of that category. Such a category was proposed by Milicic-Soergel in the 90’s. In many ways its structure looks similar to that of the classical BGG category O – there are standard, costandard, and simple objects, and they are related via parabolic Kazhdan—Lusztig polynomials. However, in other ways, Whittaker modules behave quite differently to highest weight modules. For example, standard Whittaker modules (which play the role of Verma modules), admit multiple dimensions of contravariant forms. These extra contravariant forms provide an obstacle to generalising classical category O results like the Jantzen conjecture to the Whittaker setting. In this talk, I’ll discuss some ongoing work with Jens Eberhardt (Wuppertal) where we define a Jantzen filtration for Whittaker modules, and prove that it satisfies certain semisimplicity properties.