D-dimensional spin projection operators for arbitrary type of symmetry via Brauer algebra idempotents

TL;DR

This paper introduces a novel representation of the Brauer algebra that enables the construction of spin projection operators for various symmetries using algebraic idempotents, advancing tensor space analysis.

Contribution

It develops a new class of Brauer algebra representations that facilitate the creation of spin projectors for arbitrary symmetry types, expanding algebraic tools in tensor analysis.

Findings

New representations of the Brauer algebra are identified.

Primitive orthogonal idempotents are constructed for spin projectors.

Application to tensor spaces with various symmetries is demonstrated.

Abstract

A new class of representations of the Brauer algebra that centralizes the action of orthogonal and symplectic groups in tensor spaces is found. These representations make it possible to apply the technique of building primitive orthogonal idempotents of the Brauer algebra to the construction of integer spin Behrends-Fronsdal type projectors of an arbitrary type of symmetries.