The tilting property of Whittaker averaged central sheaves

We characterize the kernel of Iwahori-Whittaker averaging in microlocal terms. Applying this to automorphic sheaves, we generalize Faergeman and Raskin’s theorem that anti-temperedness is equivalent to having irregular singular support. Moreover, using a Radon transform argument of Bezrukavnikov and Morton-Ferguson, we extend the tilting property of Whittaker averaged central sheaves to integer coefficients.