Geometric Bessel models for GSp_4 and multiplicity one

Sergey Lysenko (1)

1 IMJ - Institut de Mathématiques de Jussieu

I this paper, which is a sequel to [5], 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 multiplicity one for Bessel models. It implies a geometric Casselman-Shalika type formula for these models. We also propose a geometric framework unifying Whittaker, Waldspurger and Bessel models.

Mots clés: geometric Langlands; Bessel models

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

Sergey Lysenko. Geometric Bessel models for GSp_4 and multiplicity one. International Mathematics Research Notices, 2005, 43, pp.2657--2694. ⟨hal-00136935⟩