## Advanced Studies in Pure Mathematics

### A Weight Basis for Representations of Even Orthogonal Lie Algebras

Alexander I. Molev

#### 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

Dates
First available in Project Euclid: 20 August 2018

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