Principal series representations of direct limit groups
Principal series representations of direct limit groups
复制标题
直接极限群的主级数表示
DOI：
10.1112/s0010437x05001430
复制
发表时间：
2004
影响因子：
1.8
通讯作者：
J. Wolf
中科院分区：
文献类型：
--
作者：
J. Wolf
我们将部分全纯上同调空间上主级数表示的几何实现与紧致李群直接极限的Bott-Borel-Weil定理相结合，得到实数还原李群直接极限的主级数表示的极限。我们引入弱抛物线直接极限的概念，并将其与极限表示是 Banach 空间上的范数保持表示或 Hilbert 空间上的酉表示的条件联系起来。我们将结果专门用于对角嵌入直接极限组。最后我们讨论将结果扩展到主级数以外的调和级数极限的可能性。
We combine the geometric realization of principal series representations on partially holomorphic cohomology spaces, with the Bott–Borel–Weil theorem for direct limits of compact Lie groups, obtaining limits of principal series representations for direct limits of real reductive Lie groups. We introduce the notion of weakly parabolic direct limits and relate it to the conditions that the limit representations are norm-preserving representations on a Banach space or unitary representations on a Hilbert space. We specialize the results to diagonal embedding direct limit groups. Finally we discuss the possibilities of extending the results to limits of tempered series other than the principal series.