Geb. 20.30, SR 2.058

5.12.2024

Yuval Gorfine

15:45 Uhr

Abstract: The aim of the talk is to show that simple groups over local fields have a spectral gap absorption principle. That is, that if a representation that doesn't have almost invariant vectors is tensored with another representation, then the tensored representation still doesn't have almost invariant vectors. This property was conjectured by Uri Bader and Roman Sauer in their paper about unitary cohomology, and was proved there in some of the cases. We prove the general result. Such tensor products appear naturally when one works with restriction and induction of representations, and it is useful to know that the spectral gap is preserved. I will (try to) give a survey of the rich and beautiful theory of representations of semisimple groups, and show how to use the celebrated Langlands classification theorem, as well as some more modern results, in order to prove the theorem.