q=0时的贝特方程，M“obius反演公式和权重倍数：III。X^{（r）}_N情形
The Bethe Equation at q=0, The M"obius Inversion Formula, and Weight Multiplicities: III. The X^{(r)}_N case
摘要：
证明了U_q（X^{（r）}_N）Bethe方程在q=0时的非对角解的个数与最近引入的Q-系统的正则幂级数解的系数一致.猜想标准解是KR（Kirillov-Reshetikhin）模的特征标。这意味着非对角解的个数与权重数一致，这被解释为U_q（X^{（r）}_N）Bethe不等式在q=0处的形式完备性.
英文摘要：
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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