Moduli of metaplectic bundles on curves and Theta-sheaves
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 \tilde\Bun_G of metaplectic bundles on X. It also has a local version \tilde\Gr_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(\tilde\Gr_G) of certain perverse sheaves on \tilde\Gr_G, which act on \tilde\Bun_G by Hecke operators. A version of the Satake equivalence is proved describing Sph(\tilde\Gr_G) as a tensor category. Further, we construct a perverse sheaf on \tilde\Bun_G corresponding to the Weil representation and show that it is a Hecke eigen-sheaf.
Keywords
Cite
@article{arxiv.math/0405021,
title = {Moduli of metaplectic bundles on curves and Theta-sheaves},
author = {Sergey Lysenko},
journal= {arXiv preprint arXiv:math/0405021},
year = {2023}
}
Comments
LaTeX2e, 54 pages