Ruijsenaars' Commuting Difference Operators as Commuting Transfer Matrices
Ruijsenaars' Commuting Difference Operators as Commuting Transfer Matrices
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Ruijsenaars 的通勤差分算子作为通勤转移矩阵
DOI：
10.1007/s002200050137
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发表时间：
1995
影响因子：
2.4
通讯作者：
K. Hasegawa
中科院分区：
文献类型：
--
作者：
K. Hasegawa
翻译后摘要：对于Belavin的椭圆量子R-矩阵，我们构造了一个L-算子作为一组差分算子作用于A型权重空间上的函数。根据基本关系RLL=LLR，取L-算子的迹给出一组交换差分算子。我们证明了对于上述L-算子，这种方法给出了具有椭圆θ函数系数的Macdonald型算子，实际上等价于Ruijsenaars算子。给出了差分L-算子与Krichever Lax矩阵之间的关系，并导出了椭圆可换微分算子的一个显式公式。我们还研究了权空间上由对称θ函数张成的系统的不变子空间。
Abstract:For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on the type A weight space. According to the fundamental relation RLL=LLR, taking the trace of the L-operator gives a set of commuting difference operators. We show that for the above mentioned L-operator this approach gives Macdonald type operators with elliptic theta function coefficient, actually equivalent to Ruijsenaars' operators. The relationship between the difference L-operator and Krichever's Lax matrix is given, and an explicit formula for elliptic commuting differential operators is derived. We also study the invariant subspace for the system which is spanned by symmetric theta functions on the weight space.