• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

AG Labpratory seminar: Sergey Arkhipov

Event ended

20th October, 2017, room 306, 5:00 p.m.
W

Sergey Arkhipov (Aarhus University) with the talk Braid relations in the affine Hecke category and differential forms with logarithmic singularities

We recall the even and 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.