2016/09/11 by Chen, Tsao-Hsien
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1609.03221
In this article we prove a conjecture of Braverman-Kazhdan in \citeBK on the acyclicity of gamma sheaves in the de Rham setting. The proof relies on the techniques developed in \citeBFO on Drinfeld center of Harish-Chandra bimodules and character D-modules. As an application, we show that the functors of convolution with gamma D-modules, which can be viewed as a version of non-linear Fourier transforms, commute with induction functors and are exact on the category of admissible D-modules on a reductive group.