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• W2000997046 abstract "Let G be a connected semisimple real matrix group. It is now apparent that the representation theory of G is intimately connected with the complex geometry of the flag variety 9. By studying appropriate orbit structures on 9, we are naturally led to representation theory in the category of Harish-Chandra modules X@, or the representation theory of category (9'. The Jacquet functor J: F(9' has proved a useful tool in converting yFW problems into (9' problems, which are often more tractable. In this paper, we advance the philosophy that the complex geometry of 9, associated to yF and (9', interacts in a natural way with the functor J, leading to deep new information on the structure of Jacquet modules. This, in turn, gives new insight into the structure of certain nilpotent cohomology groups associated to Harish-Chandra modules. Our techniques are based upon many of the ideas present in the proof of the Kazhdan-Lusztig conjectures and Bernstein's proof of the Jantzen conjecture." @default.
• W2000997046 created "2016-06-24" @default.
• W2000997046 creator A5039509072 @default.
• W2000997046 creator A5047344932 @default.
• W2000997046 date "1987-01-01" @default.
• W2000997046 modified "2023-09-27" @default.
• W2000997046 title "Complex geometry and the asymptotics of Harish-Chandra modules for real reductive Lie groups. I" @default.
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• W2000997046 doi "https://doi.org/10.1090/s0002-9947-1987-0871666-5" @default.
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