Repr\'esentations de r\'eduction unipotente pour SO(2n+1), III: exemples de fronts d'onde

TL;DR

This paper computes the wave front set of certain unipotent representations of SO(2n+1) over p-adic fields, linking it to dual orthogonal orbits in Arthur's parametrization.

Contribution

It provides explicit calculations of wave front sets for anti-tempered unipotent representations of SO(2n+1), connecting representation theory with orbit duality.

Findings

Wave front sets are identified as orthogonal orbits dual to symplectic orbits.

Explicit examples of wave front sets for specific unipotent representations.

Enhances understanding of the orbit structure in p-adic representation theory.

Abstract

Let G be a group SO(2n+1) defined over a p-adic field. We compute the wave front set of the anti-tempered irreducible representations of G(F) which are of unipotent reduction. It is the orthogonal orbit dual to the symplectic orbit appearing in the Arthur's parametrization of the representation.