Analytic Bethe Ansatz for Fundamental Representations of Yangians

Details Analytic Bethe Ansatz for Fundamental Representations of Yangians Analytic Bethe Ansatz for Fundamental Representations of Yangians

1994-06-28

arxiv.org/abs/hep-th/9406180v1

Commun.Math.Phys. 173 (1995) 225-264

Physics

High Energy Physics

High Energy Physics - Theory

46 pages, Plain Tex

Scientific paper

10.1007/BF02101234

We study the analytic Bethe ansatz in solvable vertex models associated with the Yangian $Y(X_r)$ or its quantum affine analogue $U_q(X^{(1)}_r)$ for $X_r = B_r, C_r$ and $D_r$. Eigenvalue formulas are proposed for the transfer matrices related to all the fundamental representations of $Y(X_r)$. Under the Bethe ansatz equation, we explicitly prove that they are pole-free, a crucial property in the ansatz. Conjectures are also given on higher representation cases by applying the $T$-system, the transfer matrix functional relations proposed recently. The eigenvalues are neatly described in terms of Yangian analogues of the semi-standard Young tableaux.

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