Whittaker and Bessel functors for GSp_4

Sergey Lysenko (1)

1 IMJ - Institut de Mathématiques de Jussieu

The theory of Whittaker functors for GL_n is an essential technical tools in Gaitsgory's proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence. 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 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 the Waldspurger models.

Mots clés: geometric Langlands; Bessel model; Waldspurger model

Domaines: Géométrie algébrique [math.AG]; Théorie des représentations [math.RT]

Sergey Lysenko. Whittaker and Bessel functors for GSp_4. Annales de l'Institut Fourier, 2006, 56, no. 5, pp.1505--1565. ⟨hal-00136932⟩