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
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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.
- Jacques Carmona, Sur la classification des modules admissibles irreductibles, Noncommutative harmonic analysis and Lie groups (Marseille, 1982) Lecture Notes in Math., vol. 1020, Springer, Berlin, 1983, pp. 11–34 (French). MR 733459, DOI https://doi.org/10.1007/BFb0071495 KV95 A. Knapp and D. A. Vogan Jr., Cohomological Induction and Unitary Representations, Princeton University Press, Princeton, New Jersey, 1995.
- Susana A. Salamanca-Riba and David A. Vogan Jr., On the classification of unitary representations of reductive Lie groups, Ann. of Math. (2) 148 (1998), no. 3, 1067–1133. MR 1670073, DOI https://doi.org/10.2307/121036
- David A. Vogan Jr., Representations of real reductive Lie groups, Progress in Mathematics, vol. 15, Birkhäuser, Boston, Mass., 1981. MR 632407
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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
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
Article copyright:
© Copyright 2001
American Mathematical Society