Advanced Studies in Pure Mathematics

A Weight Basis for Representations of Even Orthogonal Lie Algebras

Alexander I. Molev

Full-text: Open access

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.

Article information

Source
Combinatorial Methods in Representation Theory, K. Koike, M. Kashiwara, S. Okada, I. Terada and H.-F. Yamada, eds. (Tokyo: Mathematical Society of Japan, 2000), 221-240

Dates
Received: 9 February 1999
First available in Project Euclid: 20 August 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1534789261

Digital Object Identifier
doi:10.2969/aspm/02810221

Mathematical Reviews number (MathSciNet)
MR1864482

Zentralblatt MATH identifier
1008.17003

Citation

Molev, Alexander I. A Weight Basis for Representations of Even Orthogonal Lie Algebras. Combinatorial Methods in Representation Theory, 221--240, Mathematical Society of Japan, Tokyo, Japan, 2000. doi:10.2969/aspm/02810221. https://projecteuclid.org/euclid.aspm/1534789261


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