嵌套Bethe向量的级数生成
Generating Series for Nested Bethe Vectors
摘要：
我们将离壳层$U_q(\widehat{\mathfrak{gl}}_N)$ Bethe矢量之间的嵌套关系重新表述为一个特定的方程，生成一系列的组合$U_q(\widehat{\mathfrak{gl}}_N)$电流串。利用生成级数的逆，我们发现了一种新的泛离壳Bethe向量之间的层次关系，这对Bethe方程的推导是有用的。作为应用的一个例子，我们使用这些关系的推导分析Bethe anomaly方程[Arnaudon D。例如，Ann. Henri Poincaré 7（2006），1217-1268，math-ph/0512037]，用于代数$U_q(\widehat{\mathfrak{gl}}_2)$的泛Bethe向量的参数。
英文摘要：
We reformulate nested relations between off-shell $U_q(\widehat{\mathfrak{gl}}_N)$ Bethe vectors as a certain equation on generating series of strings of the composed $U_q(\widehat{\mathfrak{gl}}_N)$ currents. Using inversion of the generating series we find a new type of hierarchical relations between universal off-shell Bethe vectors, useful for a derivation of Bethe equation. As an example of application, we use these relations for a derivation of analytical Bethe ansatz equations [Arnaudon D. et al., Ann. Henri Poincaré 7 (2006), 1217-1268, math-ph/0512037] for the parameters of universal Bethe vectors of the algebra $U_q(\widehat{\mathfrak{gl}}_2)$.
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