Whittaker and Bessel functors for GSp_4

Details Whittaker and Bessel functors for GSp_4 Whittaker and Bessel functors for GSp_4

2003-10-22

arxiv.org/abs/math/0310361v4

Mathematics

Algebraic Geometry

52 pages, final version, to appear in Ann. de l'Institut Fourier

Scientific paper

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.

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