An explicit construction of all finite-dimensional irreducible representations of classical Lie algebras is a solved problem and a Gelfand-Zetlin type basis is known. However the latter lacks the orthogonality property or does not consist of weight vectors for 𝔰𝔬(n) and 𝔰𝔭(2n). In case of Lie superalgebras all finite-dimensional irreducible representations are constructed explicitly only for 𝔤𝔩(1|n), 𝔤𝔩(2|2), 𝔬𝔰𝔭(3|2) and for the so called essentially typical representations of 𝔤𝔩(m|n). In the present paper we introduce an orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra 𝔬𝔰𝔭(1|2n) and for all irreducible covariant tensor representations of the general linear Lie superalgebra 𝔤𝔩(m|n). Expressions for the transformation of the basis under the action of algebra generators are given. The results are a step towards the explicit construction of the parastatistics Fock space.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-7,
author = {N. I. Stoilova and J. Van der Jeugt},
title = {Explicit representations of classical Lie superalgebras in a Gelfand-Zetlin basis},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {83-93},
zbl = {1275.17019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-7}
}
N. I. Stoilova; J. Van der Jeugt. Explicit representations of classical Lie superalgebras in a Gelfand-Zetlin basis. Banach Center Publications, Tome 95 (2011) pp. 83-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-7/