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Geometric Bessel models for \(\text{GSp}_4\) and multiplicity one. (English) Zbl 1088.22011

This paper studies Bessel models of representations of \(\text{GSp}_4\) in the framework of the geometric Langlands program. According to the “fonctions-faisceaux” philosophy, the Bessel module should have a geometric counterpart. The author follows the strategy of E. Frenkel, D. Gaitsgory and K. Vilonen [Ann. Math. (2) 153, No. 3, 699–748 (2001; Zbl 1070.11050)]. He proposes a general framework that gives a uniform way to define Whittaker, Waldspurger and Bessel categories. Then he studies Bessel categories and proves geometric versions of some results on Bessel models.

MSC:

22E57 Geometric Langlands program: representation-theoretic aspects
11F70 Representation-theoretic methods; automorphic representations over local and global fields

Citations:

Zbl 1070.11050
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