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Representation Theory

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Admissible nilpotent coadjoint orbits
of $p$-adic reductive Lie groups

Author: Monica Nevins
Journal: Represent. Theory 3 (1999), 105-126
MSC (1991): Primary 20G25; Secondary 22E50
Published electronically: June 22, 1999
MathSciNet review: 1698202
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Abstract: The orbit method conjectures a close relationship between the set of irreducible unitary representations of a Lie group $G$, and admissible coadjoint orbits in the dual of the Lie algebra. We define admissibility for nilpotent coadjoint orbits of $p$-adic reductive Lie groups, and compute the set of admissible orbits for a range of examples. We find that for unitary, symplectic, orthogonal, general linear and special linear groups over $p$-adic fields, the admissible nilpotent orbits coincide with the so-called special orbits defined by Lusztig and Spaltenstein in connection with the Springer correspondence.

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Additional Information

Monica Nevins
Affiliation: Department of Mathematics, University of Alberta, Edmonton, AB T6G 2G1, Canada

Keywords: Orbit method, nilpotent orbits, admissible orbits, $p$-adic groups
Received by editor(s): December 7, 1998
Received by editor(s) in revised form: February 2, 1999
Published electronically: June 22, 1999
Additional Notes: Ph.D. research supported by a teaching assistantship in the Department of Mathematics at MIT, and by an ‘NSERC 1967’ Scholarship from the Natural Sciences and Engineering Research Council of Canada. Postdoctoral research supported by the Killam Trust
Article copyright: © Copyright 1999 American Mathematical Society