The wavefront set of representations of p-adic groups

Thesis

In this thesis we study an important invariant attached to admissible smooth representations of a reductive p-adic group G called the wave- front set. Our main contribution is the study of the wavefront set over a maximal unramified extension K of the base field. In the first chapter we obtain an identity relating the wavefront set over K to the Kawanaka wavefront set of certain representations of the reductive quotient of para- horic subgroups of G. The second chapter gives a parameterisation of the nilpotent orbits over K, and endows them with new structure. The third chapter uses the Borel–Casselman equivalence to obtain an expres- sion for the wavefront set of Iwahori spherical representations in terms of the Springer correspondence, and uses it to compute the wavefront set for a class of representations of particular importance to the theory of automorphic forms.

Authors: Okada, ET

• DOI: 10.5287/ora-kzjp2gn95
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: wavefront set; p-adic groups
• Subjects: Mathematics; Lie groups; Representations of groups; Number theory