Whittaker Functors for Gsp 4 Sergey Lysenko

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 cor...

Whittaker functors for G S p 4

1.1 One of the important technical tools in D. Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([3]) is the theory of Whittaker functors for GLn. In this paper we define analogous functors for GSp4 and study their properties. Let us first review the situation at the level of automorphic forms on G = Sp4. Let X be a smooth projective absolutely i...

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 Langl...

Twisted Whittaker models for metaplectic groups

Compatibility of the Theta correspondence with the Whittaker functors

We prove in this note that the global geometric theta lifting for the pair (H,G) is compatible with the Whittaker normalization, where (H,G) = (SO2n, Sp2n), (Sp2n, SO2n+2), or (GLn, GLn+1). More precisely, let k be an algebraically closed field of characteristic p > 2. Let X be a smooth projective connected curve over k. For a stack S write D(S) for the derived category of étale constructible Q̄...