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Representation growth of p-adic analytic groups

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Margherita Piccolo
Universität Düsseldorf
Wed, 02/11/2022 - 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar


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.


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