Geometric Bessel models for GSp_4 and multiplicity one

Abstract

I this paper, which is a sequel to math.AG/0310361, we study Bessel models of representations of GSp_4 over a local non archimedian field in the framework of the geometric Langlands program. The Bessel module over the nonramified Hecke algebra of GSp_4 admits a geometric counterpart, the Bessel category of perverse sheaves on some ind-algebraic stack. We use it to prove a geometric version of the multiplicity one for Bessel models. It implies a geometric Casselman-Shalika type formula for these models. The strategy of the proof is the same as in the paper of Frenkel, Gaitsgory and Vilonen math.AG/9907133. We also propose a geometric framework unifying Whittaker, Waldspurger and Bessel models.