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NILPOTENT INVARIANTS FOR GENERIC DISCRETE SERIES OF REAL GROUPS
Part of:
Lie groups
Published online by Cambridge University Press: 24 April 2026
Abstract
Let 
$G(\mathbb {R})$ be a real reductive group. Suppose 
$\pi $ is an irreducible representation of 
$G(\mathbb {R})$ having a Whittaker model, and consider three invariants of 
$\pi $ related to nilpotent elements of the Lie algebra of G (or its dual): the associated variety, the wave-front set, and the set of Whittaker data for which 
$\pi $ has a Whittaker model. If 
$\pi $ is a discrete series representation, these invariants are known to determine each other. We provide a self-contained account of this and related matters. Many of the results were known: we give simplified proofs for several of them, for instance a simple proof (for generic discrete series) that the associated variety and the wave-front set are related by the Kostant–Sekiguchi correspondence.
MSC classification
Information
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 25 , Issue 3 , May 2026 , pp. 1651 - 1673
- Copyright
- © The Author(s), 2026. Published by Cambridge University Press
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