Algebra Seminar, by Margherita Piccolo (Heinrich Heine University, Duesseldorf)
Speaker: Margherita Piccolo (Heinrich Heine University, Duesseldorf)
Title: Representation growth of p-adic analytic groups.
Abstract: The representation growth of a group G measures the asymptotic distribution of its irreducible representations. Whenever the growth is polynomial, a suitable vehicle for studying it is a Dirichlet generating series called the representation zeta function of G. One of the key invariants in this context is the abscissa of convergence of the representation zeta function. The spectrum of all abscissae arising across a given class of groups is of considerable interest and has been studied in some cases.
In the realm of p-adic analytic groups (with perfect Lie algebra), the abscissae of convergence are explicitly known only for groups of small dimensions. But there are interesting asymptotic results for 'simple' p-adic analytic groups of increasing dimension. In this talk, I will give an overview of the main tools and ingredients in this area and I will report on recent work joint with Moritz Petschick to enlarge the class of groups.
Tid: 2022-11-30 15:15 till 16:15
anitha [dot] thillaisundaram [at] math [dot] lu [dot] se