Enumerating traceless matrices over compact discrete valuation rings

Angela Carnevale, Shai Shechter, Christopher Voll

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We enumerate traceless square matrices over finite quotients of compact discrete valuation rings by their image sizes. We express the associated rational generating functions in terms of statistics on symmetric and hyperoctahedral groups, viz. Coxeter groups of types A and B, respectively. These rational functions may also be interpreted as local representation zeta functions associated to the members of an infinite family of finitely generated class-2-nilpotent groups. As a byproduct of our work, we obtain descriptions of the numbers of traceless square matrices over a finite field of fixed rank in terms of statistics on the hyperoctahedral groups.

Original languageEnglish
Pages (from-to)957-986
Number of pages30
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - 1 Aug 2018

ASJC Scopus subject areas

  • Mathematics (all)


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