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Junior Geometry
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Joakim Asger F?rgeman, Zoom: Gaitsgory\'s construction of central sheaves on the affine flag variety
Tuesday, March 09, 2021, 03:45pm - 04:45pm
Let G be a (split) connected reductive group over a finite field $F_q$, and let $K=F_q((t))$, $O=F_q{t}$. Then a theorem of Bernstein realizes the bi-$G(O)$-invariant compactly supported functions on $G(K)$ as the center of the algebra of bi-$I$-invariant compactly supported functions on $G(K)$, where $I$ denotes the Iwahori subgroup of $G(O)$.In this talk we are going to talk about Gaitsgory's geometric version of this result. More precisely, using nearby cycles, Gaitsgory constructed a tensor functor from the symmetric monoidal category of $G(O)$-invariant perverse sheaves on the affine grassmannian to the center of the monoidal category of Iwahori-invariant perverse sheaves on the affine flag variety. Moreover, this functor satisfies a myriad of nice properties, some of which are invisible at the level of Hecke algebras.
Location: Zoom

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