Symplectic and orthogonal Lie algebra technology for bosonic and fermionic oscillator models of integrable systems
Macfarlane, A. J. ; Pfeiffer, H. ; Wagner, F.
arXiv, 0007040 / Harvested from arXiv
Text on arXiv
To provide tools, especially L-operators, for use in studies of rational Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N) (b_n, d_n) or sp(2n) (c_n) are the invariance algebras of their R matrices, this paper develops a presentation of these Lie algebras convenient for the context, and derives many properties of the matrices of their defining representations and of the ad-invariant tensors that enter their multiplication laws. Metaplectic-type representations of sp(2n) and so(N) on bosonic and on fermionic Fock spaces respectively are constructed. Concise general expressions (see (5.2) and (5.5) below) for their L-operators are obtained, and used to derive simple formulas for the T operators of the rational RTT algebra of the associated integral systems, thereby enabling their efficient treatment by means of the algebraic Bethe ansatz.
Publié le : 2000-07-31
Classification:  Mathematical Physics 
@article{0007040,
     author = {Macfarlane, A. J. and Pfeiffer, H. and Wagner, F.},
     title = {Symplectic and orthogonal Lie algebra technology for bosonic and
  fermionic oscillator models of integrable systems},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0007040}
}

Macfarlane, A. J.; Pfeiffer, H.; Wagner, F. Symplectic and orthogonal Lie algebra technology for bosonic and
  fermionic oscillator models of integrable systems. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0007040/