Non-vanishing of quantum geometric Whittaker coefficients

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.

arXiv comment31 pages, comments welcome