Decomposition numbers for Brauer algebras of type G(m,p,n) in characteristic zero

TL;DR

This paper introduces Brauer algebras linked to complex reflection groups of type G(m,p,n) and determines their decomposition numbers in characteristic zero, advancing understanding of their representation theory.

Contribution

It is the first to analyze the decomposition numbers of Brauer algebras of type G(m,p,n) in characteristic zero using Clifford theory.

Findings

Decomposition numbers for G(m,p,n) Brauer algebras are explicitly determined.

Representation theory of these algebras is characterized in characteristic zero.

New connections between complex reflection groups and Brauer algebras are established.

Abstract

We introduce Brauer algebras associated to complex reflection groups of type $G(m,p,n)$, and study their representation theory via Clifford theory. In particular, we determine the decomposition numbers of these algebras in characteristic zero.