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

Abstract

The explicit expressions of the operators of the irreducible representations of the orthogonal Cayley–Klein algebras son+1(j) are obtained from the well-known Gel’fand–Tsetlin representations of son+1. The contractions and the analytic continuations of the representations of so3(j1,j2),so4(j1, j2, j3) are regarded as examples. This approach gives the representations of the contracted and the analytically continued algebras in different bases, for example, in discrete and continuous ones. Possible contractions of the irreducible representations are discussed.