Geometric Whittaker models and Eisenstein series for Mp 2Report as inadecuate



 Geometric Whittaker models and Eisenstein series for Mp 2


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Let X be a smooth projective curve over an algebraically closed field of characteristic >2. Let Bun {Mp 2} be the stack of metaplectic bundles on X of rank 2. In this paper we study the derived category of genuine l-adic sheaves on Bun {Mp 2} in the framework of the quantum geometric Langlands. We describe the corresponding Whittaker category, develop the theory of geometric Eisenstein series and calculate the most non-degenerate Fourier coefficients of these Eisenstein series. The existing constructions of automorphic sheaves for GL n are based on using Whittaker sheaves. Our calculations lead to a conjectural characterization of the Whittaker sheaf for Mp 2, though its existence is not clear. We also formulate a conjectural relation between the quantum Langlands functors and the theta-lifting functors for the dual pair (Mp 2, PGL 2).



Author: Sergey Lysenko

Source: https://archive.org/







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