Jacobson generators, Fock representations and statistics of sl(n+1)
Abstract
The properties of A-statistics, related to the class of simple Lie algebras sl(n+1) (Palev, T.D.: Preprint JINR E17-10550 (1977); hep-th/9705032), are further investigated. The description of each sl(n+1) is carried out via generators and their relations, first introduced by Jacobson. The related Fock spaces W_p (p=1,2,...) are finite-dimensional irreducible sl(n+1)-modules. The Pauli principle of the underlying statistics is formulated. In addition the paper contains the following new results: (a) The A-statistics are interpreted as exclusion statistics; (b) Within each W_p operators B(p)_1^\pm, ..., B(p)_n^\pm, proportional to the Jacobson generators, are introduced. It is proved that in an appropriate topology the limit of B(p)_i^\pm for p going to infinity is equal to B_i^\pm, where B_i^\pm are Bose creation and annihilation operators; (c) It is shown that the local statistics of the degenerated hard-core Bose models and of the related Heisenberg spin models is p=1 A-statistics.
Keywords
Cite
@article{arxiv.hep-th/0010107,
title = {Jacobson generators, Fock representations and statistics of sl(n+1)},
author = {T. D. Palev and J. Van der Jeugt},
journal= {arXiv preprint arXiv:hep-th/0010107},
year = {2014}
}
Comments
LaTeX-file, 33 pages