Supercuspidal representations: construction, classification, and characters

2025/10/14 by Jessica Fintzen, Fintzen, Jessica
Arts and Humanities · #Archaeological and Historical Studies #Ancient Egypt and Archaeology #Archaeological and Geological Studies

paper · pdf · doi:10.48550/arxiv.2510.12883

Abstract

The building blocks for irreducible smooth representations of p-adic groups are the supercuspidal representations. In these notes that are an expansion of a lecture series given during the IHES summer school 2022 we will explore an explicit exhaustive construction of these supercuspidal representations and their character formulas and observe a striking parallel between a large class of these representations and discrete series representations of real algebraic Lie groups. A key ingredient for the construction of supercuspidal representations is the Bruhat-Tits theory and Moy-Prasad filtration, which we will recall in this survey.

Citations

• Construction of tame supercuspidal representations in arbitrary residue characteristic
• Discrete series L-packets for real reductive groups
• Reduction to depth zero for tame p-adic groups via Hecke algebra isomorphisms
• Explicit asymptotic expansions in p-adic harmonic analysis II
• A twisted Yu construction, Harish-Chandra characters, and endoscopy
• Regular supercuspidal representations
• Lie groups and Lie algebras
• Distinguished tame supercuspidal representations
• Supercuspidal representations: an exhaustion theorem

Cited by

• A depth-zero principal-series block whose Hecke algebra has a non-trivial two-cocycle

Related

• Représentations supercuspidales
• Regular supercuspidal representations
• Characterization of supercuspidal representations and very regular elements
• Simple supercuspidals and the Langlands correspondence
• Distinguished regular supercuspidal representations