Enumerating traceless matrices over compact discrete valuation rings
Carnevale, Angela
Carnevale
Angela
Shechter, Shai
Shechter
Shai
Voll, Christopher
Voll
Christopher
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.
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957-986
957-986
Hebrew Univ Magnes Press
2018