On the transverse symbol of vectorial distributions and some applications to harmonic analysis (Q1914906)

Often the first proofs on representations of semisimple Lie groups are very long and reticulated. The authors here give transparent proofs of results of Bruhat and Harish-Chandra on the irreducibility of parabolically and normally induced representations, and of Harish-Chandra in Whittaker theory. This is done by the help of the transverse symbol of vector valued distributions supported on submanifolds. For spaces of such distributions invariant under a Lie group a microlocal vanishing theorem is proved.