Commuting matrices and volumes of linear stacks

Abstract

A conjecture by Higman asserts that the number of conjugacy classes in the unipotent group of upper triangular matrices over a finite field depends polynomially on the number of elements of the field. We will study several alternative counting problems arising from quiver representations and prove explicit formulas relating the corresponding invariants to the invariants of Higman's conjecture. To do this, we develop a general framework of linear stacks over small etale sites and study volumes of these stacks and of their substacks of absolutely indecomposable objects.

arXiv comment23 pages

References in corpus (8)

• Mixed Hodge structures of configuration spaces
• A computational criterion for the Kac conjecture
• Motivic Donaldson-Thomas invariants and McKay correspondence
• On the number of points of nilpotent quiver varieties over finite fields
• Scalar extensions of triangulated categories
• On Higman's $k(U_n({\mathbb{F}}_q))$ conjecture
• Scalar Extension of Abelian and Tannakian Categories
• Moduli spaces, indecomposable objects and potentials over a finite field

Cited by in corpus (1)

• Generating series for the $E$-polynomials of $GL(n,\mathbb{C})$-character varieties