Metaplectic Whittaker category and quantum groups : the "small" FLE

TL;DR

This paper establishes an equivalence between Hecke eigensheaves in the metaplectic Whittaker category and modules over the small quantum group, advancing the quantum geometric Langlands program.

Contribution

It proves the fundamental local equivalence (FLE) in quantum geometric Langlands by linking metaplectic Whittaker categories to small quantum group modules.

Findings

Category of Hecke eigensheaves is equivalent to small quantum group modules.

Progress towards proving the fundamental local equivalence (FLE).

Supports the conjectural framework of quantum geometric Langlands.

Abstract

We prove that the category of Hecke eigensheaves in the metaplectic Whittaker category of the affine Grassmannian is equivalent to the category of modules over the small quantum group. This a step towards proving the FLE: the fundamental local equivalence in the quantum geometric Langlands theory.