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


A. I. Molev


Research Report 99-21
Date: 6 September 1999


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.

Key phrases

orthogonal Lie algebras. Gelfand-Tsetlin bases. Yangians. twisted Yangians.

AMS Subject Classification (1991)

Primary: 17B35
Secondary: 81R50


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