Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Embeddings of Harish-Chandra modules, $ {\germ n}$-homology and the composition series problem: the case of real rank one


Author: David H. Collingwood
Journal: Trans. Amer. Math. Soc. 285 (1984), 565-579
MSC: Primary 22E45; Secondary 20G05
MathSciNet review: 752491
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a connected semisimple matrix group of real rank one. Fix a minimal parabolic subgroup $ P = MAN$ and form the (normalized) principal series representations $ I_P^G(U)$. In the case of regular infinitesimal character, we explicitly determine (in terms of Langlands' classification) all irreducible submodules and quotients of $ I_P^G(U)$. As a corollary, all embeddings of an irreducible Harish-Chandra module into principal series are computed. The number of such embeddings is always less than or equal to three. These computations are equivalent to the determination of zero $ {\mathfrak{n}}$-homology.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E45, 20G05

Retrieve articles in all journals with MSC: 22E45, 20G05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0752491-X
PII: S 0002-9947(1984)0752491-X
Keywords: Representations of semisimple Lie groups, embedding theorems, composition series problem, Kazhdan-Lusztig conjectures
Article copyright: © Copyright 1984 American Mathematical Society