论文标题
与椭圆形各向异性旋转Ruijsenaars-Macdonald操作员有关的R-Matrix身份
On R-matrix identities related to elliptic anisotropic spin Ruijsenaars-Macdonald operators
论文作者
论文摘要
我们提出并证明了$ {\ rm gl} _m $ elliptic $ r $ -matrix的一组身份（在基本表示中）。在标量案例（$ m = 1 $）中，这些是S.N.M. Ruijsenaars是必要和足够的条件，用于其内核身份的基础构造的基础解决方案，用于量子无旋转的Ruijsenaars-Schneider模型。在这方面，本文的结果可以视为构建各向异性自旋ruijsenaars模型量子特征值问题解决方案的第一步。
We propose and prove a set of identities for ${\rm GL}_M$ elliptic $R$-matrix (in the fundamental representation). In the scalar case ($M=1$) these are elliptic function identities derived by S.N.M. Ruijsenaars as necessary and sufficient conditions for his kernel identity underlying construction of integral solutions to quantum spinless Ruijsenaars-Schneider model. In this respect the result of the present paper can be considered as the first step towards constructing solutions of quantum eigenvalue problem for the anisotropic spin Ruijsenaars model.
