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Explicit representations of classical Lie superalgebras in a Gelfand-Zetlin basis

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Stoilova N., Van der Jeugt J.

Banach Center Publications

2011

tom 93

nr 1

83-93

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.

Ograniczanie wyników

1 Banach Center Publications

1 Stoilova N.

1 Van der Jeugt J.

1 2011

Wyniki wyszukiwania

Explicit representations of classical Lie superalgebras in a Gelfand-Zetlin basis