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

TL;DR

This paper explores the mathematical framework of generalized quantum statistics using Lie (super)algebras, introducing A-statistics related to sl(n+1) and its applications in condensed matter physics.

Contribution

It introduces A-statistics derived from Lie algebra representations, connecting generalized quantum statistics with Lie (super)algebra theory.

Findings

A-statistics generalizes exclusion statistics.

Fock representations describe quasi-Bose statistics.

Potential applications in lattice models of condensed matter.

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.