On reducibility of parabolic induction
On reducibility of parabolic induction
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关于抛物线感应的可约性
DOI：
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发表时间：
1998
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通讯作者：
M. Tadic
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作者：
M. Tadic
可约ep-adic群的可约抛物线诱导表示的Jacquet模以与Jacquet模的传递性一致的方式约化。这个事实可以用来证明抛物线诱导表示的不可约性。经典群特别方便应用这种方法，因为我们有关于它们的Levi子群的表示理论的很好的信息（一般线性群是Levi子群的因子，因此我们可以应用Bernstein-Zelevinsky理论）。本文将这类方法应用于确定p-adic Sp（n）和SO（2n+1）的抛物诱导表示的约简问题。本文还提出了一种求不可约子元的Langlands参数的方法。在一般情况下，我们描述某些广义主级数（和其他一些有趣的抛物线诱导表示）的约化在尖点情况下的约化。当尖点约简已知时，我们得到明确的答案（例如，对于极小抛物子群中支持的表示，尖点约简是众所周知的秩一约简）。
Jacquet modules of a reducible parabolically induced representation of a reductivep-adic group reduce in a way consistent with the transitivity of Jacquet modules. This fact can be used for proving irreducibility of parabolically induced representations. Classical groups are particularly convenient for application of this method, since we have very good information about part of the representation theory of their Levi subgroups (general linear groups are factors of Levi subgroups, and therefore we can apply the Bernstein-Zelevinsky theory). In the paper, we apply this type of approach to the problem of determining reducibility of parabolically induced representations ofp-adic Sp(n) and SO(2n+1). We present also a method for getting Langlands parameters of irreducible subquotients. In general, we describe reducibility of certain generalized principal series (and some other interesting parabolically induced representations) in terms of the reducibility in the cuspidal case. When the cuspidal reducibility is known, we get explicit answers (for example, for representations supported in the minimal parabolic subgroups, the cuspidal reducibility is well-known rank one reducibility).