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 mathématiques

Intervenant-e-s

Sergei Arkhipov, Aarhus University, Danemark

entrée libre

Classement

Catégorie: Séminaire