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Intertwining operators into cohomology representations for semisimple Lie groups II


Author: Robert W. Donley Jr.
Journal: Represent. Theory 2 (1998), 278-297
MSC (1991): Primary 22E46
DOI: https://doi.org/10.1090/S1088-4165-98-00044-2
Published electronically: June 16, 1998
MathSciNet review: 1628039
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Abstract: One approach to constructing unitary representations for semisimple Lie groups utilizes analytic cohomology on open orbits of generalized flag manifolds. This work gives explicit formulas for harmonic cocycles associated to certain holomorphic homogeneous vector bundles, extending previous results of the author (Intertwining operators into cohomology representations for semisimple Lie groups, J. Funct. Anal. 151 (1997), 138-165). The key step shows that holomorphic discrete series representations and their limits are well-behaved with respect to restriction to certain submanifolds.


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Additional Information

Robert W. Donley Jr.
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Address at time of publication: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: donley@math.mit.edu

DOI: https://doi.org/10.1090/S1088-4165-98-00044-2
Received by editor(s): February 5, 1998
Received by editor(s) in revised form: March 31, 1998, and May 13, 1998
Published electronically: June 16, 1998
Additional Notes: Supported by NSF Grant DMS 9627447.
Article copyright: © Copyright 1998 American Mathematical Society

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