经典超可积$GL(3)$磁链因子的约化
Reduction of divisors for classical superintegrable $GL(3)$ magnetic chain
摘要：
由Sklyanin得到的经典$GL(3)$磁链的分离变量在亏格$g$非超椭圆代数曲线上形成一个次数为$n$的通有正因子$D$.因为$n>g$，所以该除数$D$在雅可比矩阵中具有唯一的代表性$ρ(D)$，该雅可比矩阵可以通过使用Abel算法的$|D|=n-g$步骤来构造。我们研究了相应的因子链的性质，证明了经典的$GL(3)$磁链是一个超可积系统，具有暗淡的$|D|=2$超可积哈密顿量.
英文摘要：
Variables of separation for classical $GL(3)$ magnetic chain obtained by Sklyanin form a generic positive divisor $D$ of degree $n$ on a genus $g$ non-hyperelliptic algebraic curve. Because $n>g$ this divisor $D$ has unique representative $ρ(D)$ in the Jacobian which can be constructed by using dim$|D|=n-g$ steps of Abel's algorithm. We study properties of the corresponding chain of divisors and prove that the classical $GL(3)$ magnetic chain is a superintegrable system with dim$|D|=2$ superintegrable Hamiltonians.
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