Symplectic and orthogonal Lie algebra technology for bosonic and fermionic oscillator models of integrable systems
Abstract
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.
Keywords
Cite
@article{arxiv.math-ph/0007040,
title = {Symplectic and orthogonal Lie algebra technology for bosonic and fermionic oscillator models of integrable systems},
author = {A. J. Macfarlane and H. Pfeiffer and F. Wagner},
journal= {arXiv preprint arXiv:math-ph/0007040},
year = {2011}
}
Comments
24 pages, LaTeX