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arXiv · 1603.03615

Gel'fand-Zetlin basis for a class of representations of the Lie superalgebra gl(\infty|\infty)

N. I. Stoilova·J. Van der Jeugt
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Abstract

A new, so called odd Gel'fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(n|n). The related Gel'fand-Zetlin patterns are based upon the decomposition according to a particular chain of subalgebras of gl(n|n). This chain contains only genuine Lie superalgebras of type gl(k|l) with k and l nonzero (apart from the final element of the chain which is gl(1|0)=gl(1)). Explicit expressions for a set of generators of the algebra on this Gel'fand-Zetlin basis are determined. The results are extended to an explicit construction of a class of irreducible highest weight modules of the general linear Lie superalgebra gl(\infty|\infty).

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N. I. Stoilova, J. Van der Jeugt. 2016-03-11. Gel'fand-Zetlin basis for a class of representations of the Lie superalgebra gl(\infty|\infty). https://doi.org/10.1088/1751-8113%2F49%2F16%2F165204

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