Strictly small representations and a reduction theorem for the unitary dual
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- by Susana A. Salamanca-Riba and David A. Vogan, Jr.
- Represent. Theory 5 (2001), 93-110
- DOI: https://doi.org/10.1090/S1088-4165-01-00127-3
- Published electronically: May 17, 2001
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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.References
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Bibliographic 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
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Represent. Theory 5 (2001), 93-110
- MSC (2000): Primary 22E46
- DOI: https://doi.org/10.1090/S1088-4165-01-00127-3
- MathSciNet review: 1835000