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.
orthogonal Lie algebras. Gelfand-Tsetlin bases. Yangians. twisted Yangians.
AMS Subject Classification (1991)
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