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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Intertwining operators into cohomology representations for semisimple Lie groups II
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by Robert W. Donley, Jr. PDF
Represent. Theory 2 (1998), 278-297 Request permission

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
  • MR Author ID: 625558
  • Email: donley@math.mit.edu
  • 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.
  • © Copyright 1998 American Mathematical Society
  • Journal: Represent. Theory 2 (1998), 278-297
  • MSC (1991): Primary 22E46
  • DOI: https://doi.org/10.1090/S1088-4165-98-00044-2
  • MathSciNet review: 1628039