Decomposition numbers for the cyclotomic Brauer algebras in characteristic zero

TL;DR

This paper investigates the representation theory of cyclotomic Brauer algebras in characteristic zero, focusing on their block structure and decomposition numbers through algebraic decomposition techniques.

Contribution

It introduces a method to analyze cyclotomic Brauer algebras by truncation to subalgebras, revealing their block structure and decomposition numbers in characteristic zero.

Findings

Determined the block structure of cyclotomic Brauer algebras.

Calculated decomposition numbers in characteristic zero.

Connected the algebra's structure to walled and classical Brauer algebras.

Abstract

We study the representation theory of the cyclotomic Brauer algebra via truncation to idempotent subalgebras which are isomorphic to a product of walled and classical Brauer algebras. In particular, we determine the block structure and decomposition numbers in characteristic zero.