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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

   

 

Unitary Shimura correspondences for split real groups


Authors: J. Adams, D. Barbasch, A. Paul, P. Trapa and D. A. Vogan Jr.
Journal: J. Amer. Math. Soc. 20 (2007), 701-751
MSC (2000): Primary 22E46
Published electronically: April 11, 2006
MathSciNet review: 2291917
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Abstract: We find a relationship between certain complementary series representations for nonlinear coverings of split simple groups, and spherical complementary series for (different) linear groups. The main technique is Barbasch's method of calculating some intertwining operators purely in terms of the Weyl group.


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Additional Information

J. Adams
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: jda@math.umd.edu

D. Barbasch
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: barbasch@math.cornell.edu

A. Paul
Affiliation: Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008
Email: paula@wmich.edu

P. Trapa
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: ptrapa@math.utah.edu

D. A. Vogan Jr.
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02138
Email: dav@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-06-00530-3
PII: S 0894-0347(06)00530-3
Keywords: Complementary series
Received by editor(s): September 6, 2005
Published electronically: April 11, 2006
Additional Notes: The first author was supported in part by NSF grant 0532393
The second author was supported in part by NSF grants 0070561 and 0300172
The fourth author was supported in part by NSF grant 0300106
The fifth author was supported in part by NSF grants 9721441 and 0532088
This work began during a visit in 2002 to the Institute for Mathematical Sciences, National University of Singapore. The visit was supported by the Institute and the National University of Singapore. We are grateful to our colleagues at NUS for their generous hospitality.
Article copyright: © Copyright 2006 by J. Adams, D. Barbasch, A. Paul, P. Trapa, and D. A. Vogan, Jr.