The Gel’fand–Tsetlin representations of the unitary Cayley–Klein algebras

Abstract

The explicit expressions of the operators of the irreducible representations of the unitary Cayley–Klein algebras un(j) are obtained from the well-known Gel’fand–Tsetlin representations of un . The contractions of the representations of u2(j1) and u3(j1,j2) are regarded as examples. This approach gives the representations of the contracted algebras in different bases, for example, in discrete and continuous ones. Possible contractions of the irreducible representations are discussed.