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

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).

arXiv comment21 pages

References in corpus (4)

• The parafermion Fock space and explicit so(2n+1) representations
• Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)
• A class of infinite-dimensional representations of the Lie superalgebra osp(2m+1|2n) and the parastatistics Fock space
• Parafermions, parabosons and representations of so(\infty) and osp(1|\infty)

Cited by in corpus (2)

• The $Z_2\times Z_2$-graded Lie superalgebras $pso(2n+1|2n)$ and $pso(\infty |\infty )$, and parastatistics Fock spaces
• Representations of the Lie superalgebra $B(\infty ,\infty )$ and parastatistics Fock spaces