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
DOI:
https://doi.org/10.1090/S1088-4165-05-00196-2
Published electronically:
August 11, 2005
MathSciNet review:
2167903
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.