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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Orbites Nilpotentes Sphériques et Représentations unipotentes associées: Le cas $\bf SL{\textunderscore }n$
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by Hervé Sabourin PDF
Represent. Theory 9 (2005), 468-506 Request permission

Abstract:

Let $G$ be a real simple Lie group and $\mathfrak {g}$ its Lie algebra. Given a nilpotent adjoint $G$-orbit $O$, the question is to determine the irreducible unitary representations of $G$ that we can associate to $O$, according to the orbit method. P. Torasso gave a method to solve this problem if $O$ is minimal. In this paper, we study the case where $O$ is any spherical nilpotent orbit of $sl_n({\mathbb R})$, we construct, from $O$, a family of representations of the two-sheeted covering of $SL_n({\mathbb R})$ with Torasso’s method and, finally, we show that all these representations are associated to the corresponding orbit.
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Additional Information
  • Hervé Sabourin
  • Affiliation: UMR 6086 CNRS, Département de Mathématiques, Université de Poitiers, Boulevard Marie et Pierre Curie, Téléport 2 - BP 30179, 86962 Futuroscope Chasseneuil cedex, France
  • Email: sabourin@math.univ-poitiers.fr
  • Received by editor(s): June 11, 2003
  • Received by editor(s) in revised form: April 6, 2005
  • Published electronically: August 11, 2005
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 9 (2005), 468-506
  • MSC (2000): Primary 20G05, 22E46, 22E47
  • DOI: https://doi.org/10.1090/S1088-4165-05-00196-2
  • MathSciNet review: 2167903