Jacobson generators, Fock representations and statistics of sl(n+1)
Oct, 200033 pages
Published in:
- J.Math.Phys. 43 (2002) 3850-3873
e-Print:
- hep-th/0010107 [hep-th]
DOI:
Report number:
- TWI-00-05
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Abstract: (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.Note:
- LaTeX-file, 33 pages
- algebra: SL(N)
- algebra: representation
- linear space: Fock space
- Hamiltonian formalism
- bibliography
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