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arXiv · hep-th/9506167

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

Atsuo Kuniba·Yasuhiro Ohta·Junji Suzuki
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Abstract

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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Atsuo Kuniba, Yasuhiro Ohta, Junji Suzuki. 1995-06-26. Quantum Jacobi-Trudi and Giambelli Formulae for $U_q(B_r^{(1)})$ from Analytic Bethe Ansatz. https://doi.org/10.1088/0305-4470%2F28%2F21%2F024

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