Remote Access Representation Theory
Green Open Access

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
DOI: https://doi.org/10.1090/S1088-4165-01-00127-3
Published electronically: May 17, 2001
MathSciNet review: 1835000
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 22E46

Retrieve articles in all journals with MSC (2000): 22E46


Additional Information

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

David A. Vogan Jr.
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: dav@math.mit.edu

DOI: https://doi.org/10.1090/S1088-4165-01-00127-3
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