Twisted Whittaker models for metaplectic groups

TL;DR

This paper explores twisted Whittaker models for metaplectic groups, constructing a functor to factorizable sheaves and establishing an analog of the Lusztig-Steinberg tensor product theorem in this setting.

Contribution

It introduces a functor linking twisted Whittaker categories to factorizable sheaves and proves a Lusztig-Steinberg type theorem for these models, advancing understanding of their structure.

Findings

Constructed a functor from twisted Whittaker categories to factorizable sheaves.

Proved an analog of the Lusztig-Steinberg tensor product theorem.

Described the semi-simple part of the Whittaker category as a module over the Hecke algebra.

Abstract

Let G be a reductive group (over an algebraically closed field) equipped with the metaplectic data. In this paper we study the corresponding twisted Whittaker category for G. We construct and study a functor from the latter category to the corresponding category of factorizable sheaves. It plays the role of the restriction functor from the category of representations of the big quantum group to those of the graded small quantum group. We also prove an analog in our setting of the Lusztig-Steinberg tensor product theorem for quantum groups describing the semi-simple part of the Whittaker category as a module over the Hecke algebra.