论文标题
双椭圆集成系统的特征决定因素和Manakov三重
Characteristic determinant and Manakov triple for the double elliptic integrable system
论文作者
论文摘要
使用IRF-VERTEX对应关系的交织矩阵，我们提出了一个决定性表示，以确定双椭圆形成系统的通勤汉密尔顿人的生成函数。更确切地说，它是正常有序的决定因素的比率，在经典情况下，它变成了单个决定因素。在它的帮助下，我们重现了最近建议的哈密顿人对椭圆形和椭圆形的ruijsenaars模型的表达。接下来，我们研究了我们建筑的经典对应物，该构造表达了光谱曲线和相应的$ L $ -MATRIX。该矩阵明确作为Ruijsenaars的加权平均值和/或Sklyanin型Lax矩阵，其权重为Theta函数序列定义。通过构造，$ L $ -MATRIX满足Manakov三重代表，而不是宽松的方程式。最后，我们讨论了$ l $ -matrix的分解结构。
Using the intertwining matrix of the IRF-Vertex correspondence we propose a determinant representation for the generating function of the commuting Hamiltonians of the double elliptic integrable system. More precisely, it is a ratio of the normally ordered determinants, which turns into a single determinant in the classical case. With its help we reproduce the recently suggested expression for the eigenvalues of the Hamiltonians for the dual to elliptic Ruijsenaars model. Next, we study the classical counterpart of our construction, which gives expression for the spectral curve and the corresponding $L$-matrix. This matrix is obtained explicitly as a weighted average of the Ruijsenaars and/or Sklyanin type Lax matrices with the weights as in the theta function series definition. By construction the $L$-matrix satisfies the Manakov triple representation instead of the Lax equation. Finally, we discuss the factorized structure of the $L$-matrix.
