SPHERICAL FUNCTIONS, THE COMPLEX HYPERBOLIC PLANE AND THE HYPERGEOMETRIC OPERATOR
SPHERICAL FUNCTIONS, THE COMPLEX HYPERBOLIC PLANE AND THE HYPERGEOMETRIC OPERATOR
复制标题
球函数、复双曲平面和超几何算子
DOI：
10.1142/s0129167x06003886
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发表时间：
2006
影响因子：
0.6
通讯作者：
J. Tirao
中科院分区：
文献类型：
--
作者：
P. Román;J. Tirao
本文确定了与对偶埃尔米特对称对（G，K）=（SU（3），U（2））和（SU（2，1），U（2））相关的任何K型不可约球函数Φ。这是通过将一个在u = 0处解析的真实的变量u的向量值函数H = H（u）与Φ相关联来实现的，该向量值函数H = H（u）是两个具有矩阵系数的二阶微分算子的同时本征函数。其中之一来自于G的Casimir算子，我们证明了它是共轭的超几何算子，使我们能够表示函数H的矩阵值超几何函数。对于紧对（SU（3），U（2）），该项目始于[4]。
In this paper, we determine all irreducible spherical functions Φ of any K-type associated to the dual Hermitian symmetric pairs (G, K) = (SU(3), U(2)) and (SU(2,1), U(2)). This is accomplished by associating to Φ a vector valued function H = H(u) of a real variable u, analytic at u = 0, which is a simultaneous eigenfunction of two second order differential operators with matrix coefficients. One of them comes from the Casimir operator of G and we prove that it is conjugated to a hypergeometric operator, allowing us to express the function H in terms of a matrix valued hypergeometric function. For the compact pair (SU(3), U(2)), this project was started in [4].