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

This paper completes a series devoted to explicit constructions of finite-dimensional irreducible representations of the classical Lie algebras. Here the case of odd orthogonal Lie algebras (of type B) is considered (two previous papers dealt with C and D types). A weight basis for each representation of the Lie algebra (2n + 1) is constructed. The basis vectors are parametrized by Gelfand-Tsetlin-type patterns. Explicit formulae for the matrix elements of generators of (2n + 1) in this basis are given. The construction is based on the representation theory of the Yangians.