The Bethe Equation at q=0, The M"obius Inversion Formula, and Weight Multiplicities: III. The X^{(r)}_N case
The Bethe Equation at q=0, The M"obius Inversion Formula, and Weight Multiplicities: III. The X^{(r)}_N case
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q=0 时的 Bethe 方程、M"obius 反演公式和权重重数： III. X^{(r)}_N 情况
DOI：
10.1006/jabr.2001.8774
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Z. Tsuboi
中科院分区：
文献类型：
--
作者：
A. Kuniba;T. Nakanishi;Z. Tsuboi
结果表明，q=0 时 U_q(X^{(r)}_N) Bethe 方程的非对角解的个数与最近引入的 Q 系统正则幂级数解中的系数一致。据推测，规范解是 KR (Kirillov-Reshetikhin) 模块的特征。这意味着非对角解的数量与权重重数一致，这被解释为 U_q(X^{(r)}_N) Bethe ansatz 在 q=0 时的形式完整性。
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.