Sergey Arkhipov

(Aarhus University)

(Aarhus University)

Seminar

Friday, 6 September, 2013, at 13:00-14:00, in 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 $B\backslash G/B$ 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.

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 $B\backslash G/B$ 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.

Organised by: QGM

Contact person: Jørgen Ellegaard Andersen