# A weight basis for representations of even orthogonal Lie algebras

## Author

**A. I. Molev**

## Status

Research Report 99-8

Date: 9 February 1999

## Abstract

A weight basis for each finite-dimensional irreducible representation of the
orthogonal Lie algebra o(2n) is constructed. The basis vectors are
parametrized by the D-type Gelfand-Tsetlin patterns. Explicit formulas for the
matrix elements of generators of o(2n) in this basis are given. The
construction is based on the representation theory of the Yangians and extends
our previous results for the symplectic Lie algebras.

## Key phrases

orthogonal Lie algebra. representation. Gelfand-Tsetlin basis. Yangian.

## AMS Subject Classification (1991)

Primary: 17B10

Secondary: 81R10

## Content

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