Parafermions, parabosons and representations of so(\infty) and osp(1|\infty)
High Energy Physics - Theory
2009-08-24 v1 Mathematical Physics
Group Theory
math.MP
Representation Theory
Quantum Physics
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(\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.
Keywords
Cite
@article{arxiv.0801.3909,
title = {Parafermions, parabosons and representations of so(\infty) and osp(1|\infty)},
author = {N. I. Stoilova and J. Van der Jeugt},
journal= {arXiv preprint arXiv:0801.3909},
year = {2009}
}