Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras

Abstract

This paper completes a series devoted to explicit constructions of\nfinite-dimensional irreducible representations of the classical Lie algebras.\nHere the case of odd orthogonal Lie algebras (of type B) is considered (two\nprevious papers dealt with C and D types). A weight basis for each\nrepresentation of the Lie algebra o(2n+1) is constructed. The basis vectors are\nparametrized by Gelfand--Tsetlin-type patterns. Explicit formulas for the\nmatrix elements of generators of o(2n+1) in this basis are given. The\nconstruction is based on the representation theory of the Yangians. A similar\napproach is applied to the A type case where the well-known formulas due to\nGelfand and Tsetlin are reproduced.\n