On automorphic sheaves on Bun_G

Details On automorphic sheaves on Bun_G On automorphic sheaves on Bun_G

2002-11-04

arxiv.org/abs/math/0211067v3

Mathematics

Representation Theory

30 pages, updated version

Scientific paper

Let X be a smooth projective connected curve over an algebraically closed field k of positive characteristic. Let G be a reductive group over k, \gamma be a dominant coweight for G, and E be an \ell-adic \check{G}-local system on X, where \check{G} denotes the Langlands dual group. Let \Bun_G be the moduli stack of G-bundles on X. Under some conditions on the triple (G,\gamma,E) we propose a conjectural construction of a distinguished E-Hecke automorphic sheaf on \Bun_G. We are motivated by a construction of automorphic forms suggested by Ginzburg, Rallis and Soudry in [6,7]. We also generalize Laumon's theorem ([10], Theorem 4.1) for our setting. Finally, we formulate an analog of the Vanishing Conjecture of Frenkel, Gaitsgory and Vilonen for Levi subgroups of G.

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