On the representations of Sp(p, q) and SO*(2n) unitarily induced from derived functor modules
On the representations of Sp(p, q) and SO*(2n) unitarily induced from derived functor modules
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关于由导出函子模统一导出的 Sp(p, q) 和 SO*(2n) 的表示
DOI：
10.1112/s0010437x03000629
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发表时间：
2002
影响因子：
1.8
通讯作者：
Hisayosi Matumoto
中科院分区：
文献类型：
--
作者：
Hisayosi Matumoto
得到了Sp（p，q）或SO ~*（2n）的表示由导函子模酉诱导的一个分解公式，使不可约分解问题转化为导函子模的研究.特别是，我们表明，这样的诱导表示分解成一个直和的不可约酉诱导模块从导出函子模块在一定的正则性条件下的参数。特别地，SO*（2n）和Sp（p，q）的表示由它们的抛物子群的一维酉表示导出，是不可约的。
We obtain a decomposition formula of a representation of Sp(p, q) or SO*(2n) unitarily induced from a derived functor module, which enables us to reduce the problem of irreducible decompositions to the study of derived functor modules. In particular, we show that such an induced representation is decomposed into a direct sum of irreducible unitarily induced modules from derived functor modules under some regularity condition on the parameters. In particular, representations of SO*(2n) and Sp(p, q) induced from one-dimensional unitary representations of their parabolic subgroups are irreducible.