Chennai Mathematical Institute


3:30 pm, Seminar hall
Domains of holomorphy for irreducible admissible Banach representations

Aprameyan Parthasarathy
University of Paderborn, Germany.


In this talk, we'll report on progress towards a question of B.Krotz about the holomorphic extensions of non-zero K-finite vectors of irreducible admissible Banach representations of simple real Lie groups and the relation to a distinguished domain - the so-called crown domain. We'll explain some of the main ideas - the Casselman-Wallach smooth globalisation, vanishing of matrix coefficients at infinity etc. Indeed we prove the conjecture for non-Hermitian groups with some additional growth conditions on the Banach globalisations. This is joint work with Gang Liu, Uni. Metz.