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

• Autorzy: N. I. Stoilova , J. Van der Jeugt
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 17Bxx: Lie algebras and Lie superalgebras
• 17B81: Applications to physics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 93
• Numer: 1
• Strony: 83-93

Daty

wydano

2011

Twórcy

autor

N. I. Stoilova

• Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium

autor

J. Van der Jeugt

• Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium

Identyfikatory

DOI

10.4064/bc93-0-7