Admissible nilpotent coadjoint orbits of p-adic reductive Lie groups

Nevins, Monica

doi:10.1090/S1088-4165-99-00072-2

Admissible nilpotent coadjoint orbits of p-adic reductive Lie groups
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by Monica Nevins

Represent. Theory 3 (1999), 105-126

DOI: https://doi.org/10.1090/S1088-4165-99-00072-2

Published electronically: June 22, 1999

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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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