论文标题
$（\ mathrm {su}（n+m）的矩阵球形函数，\ mathrm {s}（\ mathrm {u}（n）（n）（n）\ times \ times \ times \ mathrm {u}（m））$：两个特定类）
Matrix Spherical Functions for $(\mathrm{SU}(n+m),\mathrm{S}(\mathrm{U}(n)\times \mathrm{U}(m)))$: Two Specific Classes
论文作者
论文摘要
我们考虑与紧凑型对称对$（g，k）=（\ mathrm {su}（n+m），\ mathrm {s}（\ Mathrm {u}（n）\ Times \ Times \ Mathrm {u}（M）））的矩阵球形函数。考虑$ {\ rm u}（n）$零件中的不可约$ k $表示$（π，v）$，并且诱导的表示$ \ mathrm {ind} _k^gπ$ splate usplicity bultiusity免费。在这种情况下，研究了$ {\ rm u}（n）$零件中的不可约$ k $表示。可以根据简单的矩阵值函数近似相应的球形函数。我们可以使用差分操作员的作用来确定明确的球形函数。我们考虑了几个不可约定的$ k $表示形式，还描述了正交关系。
We consider the matrix spherical function related to the compact symmetric pair $(G,K)=(\mathrm{SU}(n+m),\mathrm{S}(\mathrm{U}(n)\times\mathrm{U}(m)))$. The irreducible $K$ representations $(π,V)$ in the ${\rm U}(n)$ part are considered and the induced representation $\mathrm{Ind}_K^Gπ$ splits multiplicity free. In this case, the irreducible $K$ representations in the ${\rm U}(n)$ part are studied. The corresponding spherical functions can be approximated in terms of the simpler matrix-valued functions. We can determine the explicit spherical functions using the action of a differential operator. We consider several cases of irreducible $K$ representations and the orthogonality relations are also described.
