Parabosons,parafermions, and explicit representations of infinite-dimensional algebras |
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Authors: | N I Stoilova and J Van der Jeugt |
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Institution: | 1.Department of Applied Mathematics and Computer Science,Ghent University,Ghent,Belgium |
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Abstract: | The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra,
for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations
of the (infinite rank) Lie algebra so(∞) and of the Lie superalgebra osp(1|∞). A complete solution to the problem is presented,
in which the Fock spaces have basis vectors labeled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation
of the basis is given explicitly. Alternatively, the basis vectors can be expressed as semi-standard Young tableaux. |
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Keywords: | |
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