Semi-orthogonal decomposition of conjugation equivariant sheaves on the loop group

Abstract: Let $k$ be an algebraically closed field and $L=k((t))$, for $G$ a connected reductive algebraic group consider $\breve G:= G(L)$. We establish a semi-orthogonal decomposition indexed by Newton strata of $D(\frac{\breve G}{\breve G})$, the DG category of $\breve G$-equivariant constructible etale sheaves on $\breve G$. In this talk I will explain (1) how to consider (ind-)constructible etale sheaves on such infinite-dimensional spaces, (2) what notion of semi-orthogonal decomposition we consider, (3) the definiton of Newton strata and the geometric input about them we need for the theory, and (4) how this category relates to the affine Hecke category. This is joint work with Xuhua He.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

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