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The Bethe Equation at q=0, The M"obius Inversion Formula, and Weight Multiplicities: III. The X^{(r)}_N case

A. Kuniba·T. Nakanishi·Z. Tsuboi
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Abstract

It is shown that the numbers of off-diagonal solutions to the U_q(X^{(r)}_N) Bethe equation at q=0 coincide with the coefficients in the recently introduced canonical power series solution of the Q-system. Conjecturally the canonical solutions are characters of the KR (Kirillov-Reshetikhin) modules. This implies that the numbers of off-diagonal solutions agree with the weight multiplicities, which is interpreted as a formal completeness of the U_q(X^{(r)}_N) Bethe ansatz at q=0.

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A. Kuniba, T. Nakanishi, Z. Tsuboi. 2001-05-17. The Bethe Equation at q=0, The M"obius Inversion Formula, and Weight Multiplicities: III. The X^{(r)}_N case. https://arxiv.org/abs/math/0105146

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