与$n$维球面相关的基本$K$型球函数
Spherical Functions of Fundamental $K$-Types Associated with the $n$-Dimensional Sphere
摘要：
本文用矩阵超几何函数描述了与$(G,K)=({\mathrm{SO}}(n+1),{\mathrm{SO}}(n))$对相关的基本$K$型不可约球函数。该描述的输出是相同$K$基本类型的不可约球面函数被编码在矩阵值正交多项式的经典序列的新示例中，其大小为$2$和$3$，相对于$[0,1]$上支持的矩阵权重$W$。证明了$W$具有二阶对称超几何算子$D$ .
英文摘要：
In this paper, we describe the irreducible spherical functions of fundamental $K$-types associated with the pair $(G,K)=({\mathrm{SO}}(n+1),{\mathrm{SO}}(n))$ in terms of matrix hypergeometric functions. The output of this description is that the irreducible spherical functions of the same $K$-fundamental type are encoded in new examples of classical sequences of matrix-valued orthogonal polynomials, of size $2$ and $3$, with respect to a matrix-weight $W$ supported on $[0,1]$. Moreover, we show that $W$ has a second order symmetric hypergeometric operator $D$.
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