Differential equations for principal series whittaker functions on SU(2,2)
Differential equations for principal series whittaker functions on SU(2,2)
复制标题
SU(2,2) 上主级数 Whittaker 函数的微分方程
DOI：
10.1016/s0019-3577(97)81553-4
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
T. Hayata
中科院分区：
文献类型：
--
作者：
T. Hayata
令SU(2,2) 为索引(2,2) 的特殊酉群。本文通过取径向部分，得到了两个显式线性偏微分方程：一个由Casimir算子得出，另一个由Schmid算子得出。属于 SU(2,2) 的不可约主级数表示的 Whittaker 函数满足微分方程组，而且当该表示的最小 K 型维数为一或二时，该系统变得完整。
Let SU(2,2) be the special unitary group of index (2,2). In this paper, two explicit linear partial differential equations are obtained: one from the Casimir operator and the other from the Schmid operator by taking their radial parts. Whittaker functions belonging to an irreducible principal series representation of SU(2,2) satisfy the system of differential equations and furthermore this system becomes holonomic when the dimension of a minimal K-type of the representation is one or two.