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This paper completes a series devoted to explicit constructions offinite-dimensional irreducible representations of the classical Lie algebras.Here the case of odd orthogonal Lie algebras (of type B) is considered (twoprevious papers dealt with C and D types). A weight basis for eachrepresentation of the Lie algebra o(2n+1) is constructed. The basis vectors areparametrized by Gelfand--Tsetlin-type patterns. Explicit formulas for thematrix elements of generators of o(2n+1) in this basis are given. Theconstruction is based on the representation theory of the Yangians. A similarapproach is applied to the A type case where the well-known formulas due toGelfand and Tsetlin are reproduced.Comment: 29 pages, Late

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