Jacobson generators, Fock representations and statistics of sl(n+1)
Palev, T. D. ; Van der Jeugt, J.
arXiv, 0010107 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-10-13
Classification:  High Energy Physics - Theory,  Condensed Matter - Statistical Mechanics,  Mathematical Physics,  Mathematics - Quantum Algebra,  Quantum Physics 
@article{0010107,
     author = {Palev, T. D. and Van der Jeugt, J.},
     title = {Jacobson generators, Fock representations and statistics of sl(n+1)},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0010107}
}

Palev, T. D.; Van der Jeugt, J. Jacobson generators, Fock representations and statistics of sl(n+1). arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0010107/