Particular class of skew orthogonal polynomials are introduced and investigated, which possess Laurent symmetry. They are also shown to appear as eigenfunctions of symplectic generalized eigenvalue problems. Furthermore, the modification of these polynomials gives some symplectic eigenvalue problem and the corresponding symplectic matrix is equivalent to butterfly matrix, which is a canonical form of symplectic matrices.

中文翻译：

---

Laurent偏斜正交多项式和相关的辛矩阵

介绍并研究了具有洛朗对称性的特殊一类倾斜正交多项式。它们还显示为辛广义特征值问题的特征函数。此外，对这些多项式的修改给出了一些辛特征值问题，相应的辛矩阵等效于蝶形矩阵，它是辛矩阵的一种规范形式。