Apparaît dans la collection : Geometric representation theory in the Langlands program - Thematic month week 2 / Théorie géométrique des représentations dans le programme de Langlands - Mois thématique sem. 2

We will start by recalling the general role of motives in geometric representation theory. Then we will introduce categories of exponential motives on partial affine flag varieties, following Gaitsgory's Kirillov model, as a generalization of the category of Iwahori-Whittaker motives. Specializing to the affine Grassmannian, we will use this to construct a motivic refinement of the geometric asselman--Shalika formula, which exists for very general base schemes and coefficients. This is joint work with Robert Cass and Jakob