Physics – Mathematical Physics
Scientific paper
2000-07-31
Int.J.Mod.Phys.A16:1199-1225,2001
Physics
Mathematical Physics
24 pages, LaTeX
Scientific paper
10.1142/S0217751X01002890
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.
Macfarlane Alan J.
Pfeiffer Hendryk
Wagner Friedrich
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