Local Langlands and character sheaves
Date/Time:10 Dec 2019 14:00
Venue: S17 #04-04 SR3
Speaker: Cheng-Chiang Tsai, Stanford University
Local Langlands and character sheaves
Let G be a connected reductive group and G^{\vee} be its dual group. For example, G=SO_{2n+1} and G^{\vee}=Sp_{2n} the symplectic group on a 2n-dimensional space. The Langlands correspondence can be interpreted as attaching monodromies to representations. Over a local or global field, to certain representation one can attach a Galois representation (or some variant of it), in other words monodromic datum over the field. While local/global Langlands is largely mysterious, over a finite field there is the Deligne-Lusztig theory and theory of character sheaves; to each irreducible representation of G(F_q) or character sheaf on G one can attache a monodromy as a semisimple element in G^{\vee}. This finite field picture is completely established by Lusztig.
In this talk, we survey three seemingly unrelated connections between the local picture (in depth-zero case) and the finite field picture, raising new questions and proposing new conjectures. There will be no theorem in this talk.
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