Séminaire Lotharingien de Combinatoire, 91B.31 (2024), 12 pp.
Masamichi Kuroda and Shuhei Tsujie
The Characteristic Quasi-Polynomials for Exceptional Well-Generated Complex Reflection Groups
Abstract.
Kamiya, Takemura, and Terao initiated the theory of the characteristic
quasi-polynomial of an integral arrangement, which is a function
counting the elements in the complement of the arrangement modulo
positive integers. The characteristic quasi-polynomials of
crystallographic root systems exhibit many interesting properties.
Recently, the authors extended the concept of the characteristic
quasi-polynomials for arrangements over a Dedekind domain, where every
residue ring with respect to nonzero ideal is finite.
In this article, we investigate the characteristic quasi-polynomials
for exceptional well-generated complex reflection groups, using the
root systems over the rings of definition introduced by Lehrer and
Taylor.
We demonstrate that a specific relation between the Coxeter numbers
and the LCM-periods of the characteristic quasi-polynomials is
generalized in this context.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
The following versions are available: