Moduli of metaplectic bundles on curves and Theta-sheaves
Sergey Lysenko
Abstract
We give a geometric interpretation of the Weil representation of the metaplectic group, placing it in the framework of the geometric Langlands program. For a smooth projective curve X we introduce an algebraic stack G of metaplectic bundles on X. It also has a local version G, which is a gerbe over the affine grassmanian of G. We define a categorical version of the (nonramified) Hecke algebra of the metaplectic group. This is a category Sph(G) of certain perverse sheaves on G, which act on G by Hecke operators. A version of the Satake equivalence is proved describing Sph(G) as a tensor category. Further, we construct a perverse sheaf on G corresponding to the Weil representation and show that it is a Hecke eigen-sheaf.
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