MIT Lie Groups Seminar

Building 2, 2-142

Speaker: Anna SzumowiczTitle: Bounding Harish-Chandra charactersAbstract: Let G be a connected reductive algebraic group over a p-adic local field F . We study the asymptotic behaviour of the trace characters θπ evaluated at a regular semisimple element of G(F ) as π varies among supercuspidal representations of G(F ). Kim, Shin and Templier conjectured that $\frac{\theta_{\pi}(\gamma)}{\deg(\pi)}$ tends to 0 when π runs over irreducible supercuspidal representations of G(F ) whose central character is unitary and the formal degree of π tends to infinity. I will sketch the proof that for G semisimple the trace character is uniformly bounded on γ under the assumption, which is believed to hold in general, that all irreducible supercuspidal representations of G(F ) are compactly induced from an open compact modulo center subgroup. If time allows I could also discuss progress on optimizing the bound.