Some calculations of centralizer rings of a complex reflection group

TL;DR

This paper investigates the structure of centralizer rings for tensor products of faithful transitive permutation representations of a specific complex reflection group, extending previous research in the area.

Contribution

It provides explicit calculations of centralizer rings for a complex reflection group, complementing prior work by Imamura-Kosuda-Oura.

Findings

Determined the structure of centralizer rings for H1 tensor representations

Extended understanding of centralizer rings in complex reflection groups

Provided explicit algebraic descriptions for the specific group H1

Abstract

Let H1 be the complex reflection group of order 96. For the tensor products of faithful transitive permutation representations of H1, we determine the structures of the centralizer rings. This complements the work of Imamura-Kosuda-Oura.