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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A cocycle formula for the quaternionic discrete series


Author: Robert W. Donley Jr.
Journal: Proc. Amer. Math. Soc. 131 (2003), 1943-1951
MSC (2000): Primary 22E46, 53C65
Published electronically: November 14, 2002
MathSciNet review: 1955285
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Abstract: Schmid's proof of the Kostant-Langlands conjecture for discrete series representations of a semisimple Lie group provides a Hilbert space realization of such representations in $L^{2}$-cohomology. We give an explicit description of these harmonic forms for the quaternionic discrete series.


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Additional Information

Robert W. Donley Jr.
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
Email: rdonley@unt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06809-0
PII: S 0002-9939(02)06809-0
Keywords: Quaternionic discrete series, harmonic forms, matrix coefficients
Received by editor(s): January 22, 2002
Published electronically: November 14, 2002
Additional Notes: The author was supported by MSRI. Research at MSRI was supported in part by NSF grant DMS-9810361
Communicated by: Rebecca Herb
Article copyright: © Copyright 2002 American Mathematical Society