Matrix Valued Orthogonal Polynomials Arising from the Complex Projective Space
Matrix Valued Orthogonal Polynomials Arising from the Complex Projective Space
复制标题
由复射影空间产生的矩阵值正交多项式
DOI：
10.1007/s00365-005-0625-6
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发表时间：
2007
影响因子：
2.7
通讯作者：
J. Tirao
中科院分区：
文献类型：
--
作者：
I. Pacharoni;J. Tirao
本文的主要目的是从U(n)的表示理论中得到满足二阶微分方程的新的矩阵值正交多项式族。给定任意正定权矩阵W(t)，可以考虑相应的矩阵值正交多项式。这些多项式将是一些对称二阶微分算子D的特征函数，只有在W(t)的非常特殊的选择下。从与对(SU（n+1)， U(n)）相关的球函数理论出发，我们得到了这些对{W，D}的新族。这些依赖于足够的整数参数，以获得超越这些情况的立即扩展。
The main purpose of this paper is to display new families of matrix valued orthogonal polynomials satisfying second-order differential equations, obtained from the representation theory of U(n). Given an arbitrary positive definite weight matrix W(t) one can consider the corresponding matrix valued orthogonal polynomials. These polynomials will be eigenfunctions of some symmetric second-order differential operator D only for very special choices of W(t). Starting from the theory of spherical functions associated to the pair (SU(n+1), U(n)) we obtain new families of such pairs {W,D}. These depend on enough integer parameters to obtain an immediate extension beyond these cases.