Title: Descent Data and Braid group actions on categories

2013.09.05 |

Date | Fri 06 Sep |

Time | 13:00 — 14:00 |

Location | Aud. D4 (1531-219) |

**Abstract:**

We recall the classical notions of the degenerate Hecke algebra and of Demazure operators acting on the K-theory of a G-variety X, with G being a reductive algebraic group.

Then we propose a categorification of the algebra generated by Demazure operators and introduce the notion of Demazure Descent Data (DDD) on a category. We explain how DDD arises naturally from a monoidal action of the tensor category of quasicoherent sheaves on B\G/B on a category. A natural example of such picture is provided by the category of quasicoherent sheaves on X/G for a scheme X with an action of the reductive group G.

Next we replace the category of quasicoherent sheaves by the one of modules over the De Rham algebra Omega(X). We explain how an analog of the construction above gives rise to a braid group action of a category.