On the composition series of the standard Whittaker (g,K)-modules
On the composition series of the standard Whittaker (g,K)-modules
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关于标准 Whittaker (g,K) 模的组成系列
DOI：
10.1090/s0002-9947-2012-05801-6
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Kenji Taniguchi
中科院分区：
文献类型：
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作者：
Kensuke Kondo;Kyo Nishiyama;Hiroyuki Ochiai;Kenji Taniguchi;Kenji Taniguchi
对于实数还原线性李群，Whittaker 函数的空间是由 Iwasawa 幂零子群的非简并酉性质导出的表示空间。定义了标准 Whittaker 模块，它们是 Whittaker 函数空间的可接受子模块。当表征它们的无穷小字符是通用的时，我们首先确定它们的结构。作为积分情况的一个例子，当 是群且无穷小特征是正则积分时，我们确定了标准 Whittaker 模的复合级数。参考
For a real reductive linear Lie group, the space of Whittaker functions is the representation space induced from a non-degenerate unitary character of the Iwasawa nilpotent subgroup. Defined are the standard Whittaker-modules, which are-admissible submodules of the space of Whittaker functions. We first determine the structures of them when the infinitesimal characters characterizing them are generic. As an example of the integral case, we determine the composition series of the standard Whittaker-module whenis the groupand the infinitesimal character is regular integral. References