A characteristic-free decomposition of tensor space as a Brauer algebra module

TL;DR

This paper presents a characteristic-free method to decompose tensor space as a module over the Brauer algebra, enhancing understanding of its structure regardless of field characteristic.

Contribution

It introduces a new characteristic-free decomposition of tensor space as a Brauer algebra module, broadening applicability across different algebraic settings.

Findings

Decomposition valid for all field characteristics

Provides explicit module structure description

Advances representation theory of Brauer algebras

Abstract

We obtain a characteristic-free decomposition of tensor space, regarded as a module for the Brauer centralizer algebra.