Geometric Eisenstein series: twisted setting

2014/09/14 by Lysenko, Sergey
#11R39 #14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1409.4071

Abstract

Let G be a simple simply-connected group over an algebraically closed field k, X be a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on the moduli stack Bun_G of G-torsors on X in the setting of the quantum geometric Langlands program (for étale l-adic sheaves) in analogy with [3]. We calculate the intersection cohomology sheaf on the version of Drinfeld compactification in our twisted setting. In the case G=SL₂ we derive some results about the Fourier coefficients of our Eisenstein series. In the case of G=SL₂ and X=P¹ we also construct the corresponding theta-sheaves and prove their Hecke property.

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