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 | References | Similar Articles | Additional Information

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