Whittaker and Bessel functors for GSp_4

Abstract

One of the important technical tools in Gaitsgory's proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([3]) is the theory of Whittaker functors for GL_n. We define Whittaker functors for GSp_4 and study their properties. In a sense, these functors correspond to the maximal parabolic subgroup of GSp_4, whose unipotent radical is not commutative. We also study similar functors corresponding to the Siegel parabolic subgroup of GSp_4, they are related with Bessel models for GSp_4 and Waldspurger models for GL_2. We define the Waldspurger category, which is a geometric counterpart of the Waldspurger module over the Hecke algebra of GL_2. We prove a geometric version of the multiplicity one result for Waldspurger models.