Embeddings of Harish-Chandra modules, $\mathfrak {n}$-homology and the composition series problem: the case of real rank one
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- by David H. Collingwood PDF
- Trans. Amer. Math. Soc. 285 (1984), 565-579 Request permission
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
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 285 (1984), 565-579
- MSC: Primary 22E45; Secondary 20G05
- DOI: https://doi.org/10.1090/S0002-9947-1984-0752491-X
- MathSciNet review: 752491