For any adjoint reductive group at rational Kac-Moody level, cuspidal twisted D-modules with nilpotent singular support have at least one nonzero quantum Whittaker coefficient, proved microlocally.
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Non-vanishing of quantum geometric Whittaker coefficients
For any adjoint reductive group at rational Kac-Moody level, cuspidal twisted D-modules with nilpotent singular support have at least one nonzero quantum Whittaker coefficient, proved microlocally.