关于局部解析主级数表示不可约性
表示论
2011-01-19 v3
摘要
设 G 为 p 进连通约化群，其李代数为 g。对 G 中的抛物子群 P 以及 P 的有限维局部解析表示 V，我们研究诱导的局部解析 G 表示 W = Ind^G_P(V)。我们的结果如下关于 W 拓扑不可约性的判别准则：若对偶表示 V' 相伴的 Verma 模 U(g) \otimes_{U(p)} V' 不可约，则 W 也是拓扑不可约的。
引用
@article{arxiv.math/0612809,
title = {On the irreducibility of locally analytic principal series representations},
author = {S. Orlik and M. Strauch},
journal= {arXiv preprint arXiv:math/0612809},
year = {2011}
}
备注
44 pages; final version. An appendix has been added in which it is shown that the canonical maps between certain completions of distribution algebras are injective. This fills a gap in a previous version; it was pointed out to us by a referee