论文标题
为椭圆形的ruijsenaars差异操作员建造本本征函数
Construction of eigenfunctions for the elliptic Ruijsenaars difference operators
论文作者
论文摘要
我们提供了定义椭圆形Ruijsenaars系统的通勤差异家族的两种本征函数的扰动结构。第一种对应于MacDonald多项式的椭圆形变形，第二种是先前在三角法案中构建的渐近自由本征函数。我们将这些本征函数作为无限序列获得，如我们所示，在变量和参数的合适域中收敛。我们的结果表明，对于椭圆形的Ruijsenaars运算符定义相对论量子机械系统的领域，麦克唐纳多项式的椭圆形变形提供了相对于相关标量产品的正交功能的家族。
We present a perturbative construction of two kinds of eigenfunctions of the commuting family of difference operators defining the elliptic Ruijsenaars system. The first kind corresponds to elliptic deformations of the Macdonald polynomials, and the second kind generalizes asymptotically free eigenfunctions previously constructed in the trigonometric case. We obtain these eigenfunctions as infinite series which, as we show, converge in suitable domains of the variables and parameters. Our results imply that, for the domain where the elliptic Ruijsenaars operators define a relativistic quantum mechanical system, the elliptic deformations of the Macdonald polynomials provide a family of orthogonal functions with respect to the pertinent scalar product.
