On a class of Fock-like representations for Lie Superalgebras

Details On a class of Fock-like representations for Lie Superalgebras On a class of Fock-like representations for Lie Superalgebras

2011-04-04

arxiv.org/abs/1104.0696v1

Mathematics

Representation Theory

15 pages, Work done during postdoctoral stay of the first author, at IFM, UMSNH, Morelia, Michoacan, Mexico (in progress)

Scientific paper

Utilizing previous results of ours, on Lie superalgebra realizations via a copy of $gl(m/n)$ isomorphically embedded into the Relative Parabose Set algebra $P_{BF}$, combined with results from other authors on the Fock-space structure of $P_{BF}^{(1,1)}$ (for the special case of a single parabosonic and a single parafermionic degree of freedom), we proceed to the construction of a class of Fock-like representations for Lie superalgebras: these are infinite dimensional, decomposable representations and can be constructed for any Lie superalgebra $L$, provided we have at hand a 2-dimensional, $\mathbb{Z}_{2}$-graded representation of $L$. We further proceed into decomposing the obtained representations into finite dimensional, submodules.

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