具有拟指数核的XXX或Gaudin转移矩阵的生成算子
Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel
摘要：
设$M$是有限维多项式赋值Yangian $Y(gl_N)$ -模的张量积.考虑通用差分算子$D = \sum_{k=0}^N (-1)^k T_k(u) e^{-k\partial_u}$，其系数$T_k(u): M \to M$是与$M$相关联的XXX传递矩阵。证明了$M$值函数$f$的差分方程$Df = 0$具有由拟指数项组成的解的基.我们证明了同样的通用微分算子$D = \sum_{k=0}^N (-1)^k S_k(u) \partial_u^{N-k}$，其系数$S_k(u) : M \to M$的Gaudin转移矩阵与张量积$M$有限维多项式评估$gl_N[x]$ -模块。
英文摘要：
Let $M$ be the tensor product of finite-dimensional polynomial evaluation Yangian $Y(gl_N)$-modules. Consider the universal difference operator $D = \sum_{k=0}^N (-1)^k T_k(u) e^{-k\partial_u}$ whose coefficients $T_k(u): M \to M$ are the XXX transfer matrices associated with $M$. We show that the difference equation $Df = 0$ for an $M$-valued function $f$ has a basis of solutions consisting of quasi-exponentials. We prove the same for the universal differential operator $D = \sum_{k=0}^N (-1)^k S_k(u) \partial_u^{N-k}$ whose coefficients $S_k(u) : M \to M$ are the Gaudin transfer matrices associated with the tensor product $M$ of finite-dimensional polynomial evaluation $gl_N[x]$-modules.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
