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

A. I. Molev
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Abstract

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 o(2n+1) is constructed. The basis vectors are parametrized by Gelfand--Tsetlin-type patterns. Explicit formulas for the matrix elements of generators of o(2n+1) in this basis are given. The construction is based on the representation theory of the Yangians. A similar approach is applied to the A type case where the well-known formulas due to Gelfand and Tsetlin are reproduced.

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A. I. Molev. 1999-09-06. Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras. https://doi.org/10.1088/0305-4470%2F33%2F22%2F316

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