Geometric Whittaker models and Eisenstein series for Mp₂

2012/11/07 by Lysenko, Sergey
#11R39 #14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1211.1596

Abstract

Let X be a smooth projective curve over an algebraically closed field of characteristic >2. Let Bun_Mp2 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_Mp2 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 Mp₂, 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 (Mp₂, PGL₂).

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