0 A ug 2 00 4 Whittaker and Bessel functors for G S p 4

1.1 Whittaker and Bessel models are of importance in the theory of automorphic representations of GSp4. This paper is the first in a series of two, where we study some phenomena corresponding to these models in the geometric Langlands program. The theory of Whittaker functors for GLn is an essential technical tool in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([5]). First part of our results is an analog of this theory for GSp4. Let us first remind some facts about automorphic forms on G = Sp4. Let X be a smooth projective absolutely irreducible curve over Fq, F = Fq(X) and A be the adeles ring of F . Let B be a Borel subgroup of G and U ⊂ B its unipotent radical. For a character ψ : U(F )\U(A) → C∗ one has a global Whittaker module over G(A)