Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, II: Groups of type F, G, and H

Abstract

This is the second of two papers introducing and investigating two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. In the first part, we proved some of their properties such as rationality and functional equations. Here, we calculate such bivariate zeta functions of three infinite families of nilpotent groups of class 2 generalising the Heisenberg group of three by three unitriangular matrices over rings of integers of number fields. The local factors of these zeta functions are also expressed in terms of sums over finite hyperoctahedral groups, which provides formulae for joint distributions of three statistics on such groups.

35 pages. Preprint of an article published in the International Journal of Algebra and Computation

References in corpus (4)

• The average size of the kernel of a matrix and orbits of linear groups
• Proof of a conjecture of Klopsch-Voll on Weyl groups of type $A$
• Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, I: Arithmetic properties
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Cited by in corpus (6)

• The average size of the kernel of a matrix and orbits of linear groups
• The average size of the kernel of a matrix and orbits of linear groups, II: duality
• Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, I: Arithmetic properties
• Univariate and bivariate zeta functions of unipotent group schemes of type $G$
• Analytic properties of bivariate representation and conjugacy class zeta functions of finitely generated nilpotent groups
• Twisted conjugacy in soluble arithmetic groups