Non-vanishing of quantum geometric Whittaker coefficients

TL;DR

This paper proves that cuspidal automorphic twisted D-modules for any adjoint type reductive group have non-zero quantum Whittaker coefficients, offering a microlocal interpretation under certain conditions.

Contribution

It establishes the non-vanishing of quantum Whittaker coefficients for a broad class of automorphic D-modules and introduces a microlocal perspective on these coefficients.

Findings

Quantum Whittaker coefficients are non-zero for cuspidal automorphic twisted D-modules.

Provides a microlocal interpretation of quantum Whittaker coefficients.

Applies to any reductive group of adjoint type.

Abstract

We prove that for any reductive group $G$ of adjoint type cuspidal automorphic twisted D-modules have non-vanishing quantum Whittaker coefficients. The argument provides a microlocal interpretation of quantum Whittaker coefficients for any $\check{\Lambda}^+$-valued divisor under some hypothesis on singular support.