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Orbites Nilpotentes Sphériques et Représentations unipotentes associées: Le cas $\bf SL{\textunderscore }n$

Author: Hervé Sabourin
Journal: Represent. Theory 9 (2005), 468-506
MSC (2000): Primary 20G05, 22E46, 22E47
Published electronically: August 11, 2005
MathSciNet review: 2167903
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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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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

Received by editor(s): June 11, 2003
Received by editor(s) in revised form: April 6, 2005
Published electronically: August 11, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.