Braid relations in the affine Hecke category and differential forms with logarithmic singularities (Sergei Arkhipov, Aarhus University, Danemark)
23.03.2018 10:00
Abstract: We recall the even and the odd algebro-geometric realizations of the affine Hecke category - one via equivariant coherent sheaves on the Steinberg variety and the other in terms of some equivariant DG-modules over the DG-algebra of differential forms on a reductive group G.
The latter one has a toy analog called the coherent Hecke category. It contains certain canonical objects satisfying braid relations via convolution. The proof uses simple facts from the geometry of Bott-Samelson varieties.
Our goal is to provide a similar proof of braid relations in the affine Hecke category. It turns out that canonical braid group generators are given by certain DG-modules of logarithmic differential forms and braid relations follow immediately from a general statement which seems to be new: direct image of the DG-module of logarithmic differential forms does not depend on a resolution of singularities.
Time permitting, we will discuss three equivalent approaches to define the derived category of equivariant DG-modules.
Lieu
Bâtiment: Battelle
Séminaire de la Tortue
Organisé par
Section de mathématiquesIntervenant-e-s
Sergei Arkhipov, Aarhus University, Danemarkentrée libre
Classement
Catégorie: Séminaire