Enumerating traceless matrices over compact discrete valuation rings

Carnevale A, Shechter S, Voll C (2018)
Israel Journal of Mathematics 227(2): 957-986.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
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.
Erscheinungsjahr
Zeitschriftentitel
Israel Journal of Mathematics
Band
227
Ausgabe
2
Seite(n)
957-986
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Carnevale A, Shechter S, Voll C. Enumerating traceless matrices over compact discrete valuation rings. Israel Journal of Mathematics. 2018;227(2):957-986.
Carnevale, A., Shechter, S., & Voll, C. (2018). Enumerating traceless matrices over compact discrete valuation rings. Israel Journal of Mathematics, 227(2), 957-986. doi:10.1007/s11856-018-1755-4
Carnevale, A., Shechter, S., and Voll, C. (2018). Enumerating traceless matrices over compact discrete valuation rings. Israel Journal of Mathematics 227, 957-986.
Carnevale, A., Shechter, S., & Voll, C., 2018. Enumerating traceless matrices over compact discrete valuation rings. Israel Journal of Mathematics, 227(2), p 957-986.
A. Carnevale, S. Shechter, and C. Voll, “Enumerating traceless matrices over compact discrete valuation rings”, Israel Journal of Mathematics, vol. 227, 2018, pp. 957-986.
Carnevale, A., Shechter, S., Voll, C.: Enumerating traceless matrices over compact discrete valuation rings. Israel Journal of Mathematics. 227, 957-986 (2018).
Carnevale, Angela, Shechter, Shai, and Voll, Christopher. “Enumerating traceless matrices over compact discrete valuation rings”. Israel Journal of Mathematics 227.2 (2018): 957-986.