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VOL. 28 | 2000 A Weight Basis for Representations of Even Orthogonal Lie Algebras
Alexander I. Molev

Editor(s) Kazuhiko Koike, Masaki Kashiwara, Soichi Okada, Itaru Terada, Hiro-Fumi Yamada

Abstract

A weight basis for each finite-dimensional irreducible representation of the orthogonal Lie algebra $\mathfrak{o}(2n)$ is constructed. The basis vectors are parametrized by the $D$-type Gelfand–Tsetlin patterns. The basis is consistent with the chain of subalgebras ${\mathfrak{g}}_1 \subset \cdots \subset {\mathfrak{g}}_n$, where ${\mathfrak{g}}_k = \mathfrak{o}(2k)$. Explicit formulas for the matrix elements of generators of $\mathfrak{o}(2n)$ 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.

Information

Published: 1 January 2000
First available in Project Euclid: 20 August 2018

zbMATH: 1008.17003
MathSciNet: MR1864482

Digital Object Identifier: 10.2969/aspm/02810221

Rights: Copyright © 2000 Mathematical Society of Japan

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