M ay 2 00 5 Whittaker and Bessel functors for G S p 4

The theory of Whittaker functors for GLn is an essential technical tools in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([5]). We define Whittaker functors for GSp 4 and study their properties. 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 GL2. We define the Waldspurger category, which is a geometric counterpart of the Waldspurger module over the Hecke algebra of GL2. We prove a geometric version of the multiplicity one result for the Waldspurger models.