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Quasiboson representations of sl(n+1) and generalized quantum statistics

T. D. Palev·J. Van der Jeugt
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Abstract

Generalized quantum statistics will be presented in the context of representation theory of Lie (super)algebras. This approach provides a natural mathematical framework, as is illustrated by the relation between para-Bose and para-Fermi operators and Lie (super)algebras of type B. Inspired by this relation, A-statistics is introduced, arising from representation theory of the Lie algebra A_n. The Fock representations for A_n=sl(n+1) provide microscopic descriptions of particular kinds of exclusion statistics, which may be called quasi-Bose statistics. It is indicated that A-statistics appears to be the natural statistics for certain lattice models in condensed matter physics.

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T. D. Palev, J. Van der Jeugt. 2000-09-14. Quasiboson representations of sl(n+1) and generalized quantum statistics. https://arxiv.org/abs/hep-th/0009108

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