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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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
Published electronically: May 17, 2001


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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Bibliographic Information
  • Susana A. Salamanca-Riba
  • Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-0001
  • Email:
  • David A. Vogan, Jr.
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • Email:
  • 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:
  • MathSciNet review: 1835000