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Representation Theory

ISSN 1088-4165



Strictly small representations and a reduction theorem for the unitary dual

Authors: Susana A. Salamanca-Riba and David A. Vogan, Jr.
Journal: Represent. Theory 5 (2001), 93-110
MSC (2000): Primary 22E46
Published electronically: May 17, 2001
MathSciNet review: 1835000
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Abstract: To any irreducible unitary representation $X$ of a real reductive Lie group we associate in a canonical way, a Levi subgroup $G_{su}$ and a representation of this subgroup. Assuming a conjecture of the authors on the infinitesimal character of $X$, we show that $X$ is cohomologically induced from a unitary representation of the subgroup $G_{su}$. This subgroup is in some cases smaller than the subgroup $G_{u}$ that the authors attached to $X$ in earlier work. In those cases this provides a further reduction to the classification problem.

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Additional Information

Susana A. Salamanca-Riba
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-0001

David A. Vogan, Jr.
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Received by editor(s): December 1, 2000
Received by editor(s) in revised form: March 30, 2001
Published electronically: May 17, 2001
Additional Notes: Supported in part by NSF grant DMS-9721441
Article copyright: © Copyright 2001 American Mathematical Society