Relation between the boson calculus and Zhelobenko's method

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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.

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