APRG Seminar: 2024-10-30 - Pritam Ganguly

math.iisc.ac.i...
Speaker: Pritam Ganguly (Universität Paderborn, Germany)
Title: Norms on Harish-Chandra modules
Abstract:
In this talk, we plan to explore the natural question of how to compare different G-continuous norms on a Harish-Chandra module with a fixed growth rate. We demonstrate that the space of equivalence classes of these norms features both maximal and minimal elements, as well as a natural Sobolev distance. This leads to a new invariant, which we term the “Sobolev gap.” We will also discuss the natural question of estimating the Sobolev gap uniformly over all irreducible Harish-Chandra modules, offering a quantitative version of the Casselman-Wallach globalization theorem. Additionally, we provide explicit values for the Sobolev gap in the case of Harish-Chandra modules for SL(2,\R).