Quantum Jacobi-Trudi and Giambelli Formulae for $U_q(B_r^{(1)})$ from Analytic Bethe Ansatz

Details Quantum Jacobi-Trudi and Giambelli Formulae for $U_q(B_r^{(1)})$ from Analytic Bethe Ansatz Quantum Jacobi-Trudi and Giambelli Formulae for $U_q(B_r^{(1)})$ from Analytic Bethe Ansatz

1995-06-26

arxiv.org/abs/hep-th/9506167v1

J.Phys. A28 (1995) 6211-6226

Physics

High Energy Physics

High Energy Physics - Theory

Plain Tex(macro included), 18 pages. 7 figures are compressed and attached

Scientific paper

10.1088/0305-4470/28/21/024

Analytic Bethe ansatz is executed for a wide class of finite dimensional $U_q(B^{(1)}_r)$ modules. They are labeled by skew-Young diagrams which, in general, contain a fragment corresponding to the spin representation. For the transfer matrix spectra of the relevant vertex models, we establish a number of formulae, which are $U_q(B^{(1)}_r)$ analogues of the classical ones due to Jacobi-Trudi and Giambelli on Schur functions. They yield a full solution to the previously proposed functional relation ($T$-system), which is a Toda equation

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