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

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

1999-09-06

arxiv.org/abs/math/9909034v1

J. Phys. A: Math. Gen. 33 (2000), 4143--4168.

Mathematics

Quantum Algebra

29 pages, Latex

Scientific paper

10.1088/0305-4470/33/22/316

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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