Feb 23 at 17:30 in 507

Title: Weight modules and Kazhdan-Laumon category O.

Abstract: In work of Mathieu and Fernando the modules of the enveloping algebra with finite dimensional weight spaces are understood. These conditions can be translated into a support condition for the associated graded or some singular support condition for some sheaves on G/B. This singular support is given by taking the union of W copies of the conditions for category O. In work of Kazhdan and Laumon, they construct a category by glueing W copies of the category of perverse sheaves on G/U . This category was studied by Bezrukavnikov, Polishchuk and Morton-Ferguson. In particular some subcategory known as Kazhdan-Laumon category O was related to the representation theory of the small quantum group u_q. In joint work with Morton-Ferguson we relate the Kazhdan-Laumon category O to some subcategory of weight modules. This connection should explain the relation to the representation theory of u_q. In this talk I will present Kazhdan-Laumon’s category O construction and describe the relation with weight modules. Time permitting, Iwill discuss the connection to representation theory of the small quantum group uq via the joint work with Bezrukavnikov, McBreen and Yun and the the geometry of affine Springer fibers.