Derived functor modules arising as large irreducible constituents of degenerate principal series
Derived functor modules arising as large irreducible constituents of degenerate principal series
复制标题
DOI：
10.1112/s0010437x0600248x
复制
发表时间：
2007-01
影响因子：
1.8
通讯作者：
Hisayosi Matumoto;Peter E. Trapa
中科院分区：
文献类型：
--
作者：
Hisayosi Matumoto;Peter E. Trapa
对于群$G={\mathrm{Sp}}（p，q），\ \mathrm{SO}^\ast（2n）$，和$\mathrm{U}（m，n）$，我们考虑退化主级数，其无穷小特征符合$G$的有限维表示.我们证明了每个极大Gelfand-Kirillov维数的不可约成分是一个导函子模。我们还表明，在一个适当的“最奇异”参数，每个不可约成分是弱单幂和unitarizable。相反，我们表明，任何弱幂幺表示相关联的一个真实的形式的相应的理查森轨道是唯一的同构，可以嵌入到一个退化的主要系列在最奇异的积分参数（除了极少数的情况下，甚至在D型）。我们还讨论了导函子模到退化主级数的楔边型嵌入。
For the groups $G={\mathrm{Sp}}(p,q),\ \mathrm{SO}^\ast(2n)$, and $\mathrm{U}(m,n)$, we consider degenerate principal series whose infinitesimal character coincides with a finite-dimensional representation of $G$. We prove that each irreducible constituent of maximal Gelfand–Kirillov dimension is a derived functor module. We also show that at an appropriate ‘most singular’ parameter, each irreducible constituent is weakly unipotent and unitarizable. Conversely we show that any weakly unipotent representation associated to a real form of the corresponding Richardson orbit is unique up to isomorphism and can be embedded into a degenerate principal series at the most singular integral parameter (apart from a handful of very even cases in type D). We also discuss edge-of-wedge-type embeddings of derived functor modules into degenerate principal series.