Algebra and Geometry Seminar

Let G be a p-adic reductive group. J.-L. Kim, S. W. Shin and N. Templier conjectured that for every regular element \gamma of G, the trace character \theta_\pi (\gamma) grows much faster than deg(\pi) when deg(\pi) tends to infinity and \pi runs over irreducible supercuspidal representations of G. J.-L. Kim, S.W Shin and N. Templier proved the conjecture under some additional conditions. We discuss the further progress on the problem.