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

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.