Parafermions, parabosons and representations of so(\infty) and osp(1|\infty)

Details Parafermions, parabosons and representations of so(\infty) and osp(1|\infty) Parafermions, parabosons and representations of so(\infty) and osp(1|\infty)

2008-01-25

arxiv.org/abs/0801.3909v1

Int.J.Math.20:693-715,2009

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1142/S0129167X09005467

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(\infty) and of the Lie superalgebra osp(1|\infty). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labelled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. We also present expressions for the character of the Fock space representations.

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