Bethe Equation at q=0, Moebius Inversion Formula, and Weight Multiplicities: II. X_n case
Bethe Equation at q=0, Moebius Inversion Formula, and Weight Multiplicities: II. X_n case
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q=0 时的贝特方程、莫比乌斯反演公式和权重重数： II．
DOI：
10.1007/978-1-4612-1378-9_6
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发表时间：
2000
影响因子：
0.9
通讯作者：
T. Nakanishi
中科院分区：
文献类型：
--
作者：
A. Kuniba;T. Nakanishi
我们研究以具有一定收敛性的递归关系系统（Q系统）为特征的幂级数族。我们证明级数的系数由正式计数 U_q(X^{(1)}_n) Bethe 方程在 q=0 处的非对角解的数字表示。该级数被推测为某个不可约有限维 U_q(X^{(1)}_n) 模族的 X_n 特征，我们称之为 KR（基里洛夫-列谢蒂欣）模。在上述猜想下，这些系数给出了KR模张量积的权重重数公式，这也被解释为XXZ型Bethe向量的形式完备性。
We study a family of power series characterized by a system of recursion relations (Q-system) with a certain convergence property. We show that the coefficients of the series are expressed by the numbers which formally count the off-diagonal solutions of the U_q(X^{(1)}_n) Bethe equation at q=0. The series are conjectured to be the X_n-character of a certain family of irreducible finite-dimensional U_q(X^{(1)}_n) -modules which we call the KR (Kirillov-Reshetikhin) modules. Under the above conjecture, these coefficients give a formula of the weight multiplicities of the tensor products of the KR modules, which is also interpreted as the formal completeness of the XXZ-type Bethe vectors.