Relation between the boson calculus and Zhelobenko's method

Abstract

A comparison is made between the method of constructing finite‐dimensional representations of the classical groups using the boson calculus in its standard or modified form and the method of Zhelobenko, which uses polynomials over a homogeneous space defined by a certain triangular subgroup. It is shown that the two methods can be directly related, so that one construction can be mapped into the other.