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

## Author

**A. I. Molev**

## Status

Research Report 99-21

Date: 6 September 1999

## 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.

## Key phrases

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

## AMS Subject Classification (1991)

Primary: 17B35

Secondary: 81R50

## Content

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