Symmetric and unitary group representations. I. Duality theory

Abstract

An extension of the Schur-Weyl duality connecting the representations of the symmetric and unitary groups is given. The Schur-Weyl basis is constructed using annihilation and creation operators. Three factorisation lemmas are derived. Their importance lies in the fact that they relate the phase freedoms within the Racah-Wigner algebra of the symmetric groups and the unitary groups. Extensions of the Regge symmetries are also given. These are expressed in five duality relations.