Wave Front Sets of Nilpotent Lie Group Representations

2021/03/04 by Budde, Julia, Weich, Tobias
#Analysis of PDEs (math.AP) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2103.02968

Abstract

Let G be a nilpotent, connected, simply connected Lie group with Lie algebra \mathfrak g, and π a unitary representation of G. The goal is to prove that the wave front set of π coincides with the asymptotic cone of the orbital support of π, i.e. WF(π)=AC(\bigcup_{σ∈ supp(π)}\mathcal O_σ), where \mathcal O_σ⊂ i\mathfrak g^∗ is the coadjoint orbit associated to the irreducible unitary representation σ∈ G by Kirillov.

Related

• Wave-front sets for p-adic Lie algebras
• Orbites Nilpotentes Sphériques et Représentations unipotentes associées : Le cas SL_n
• The wavefront set: bounds for the Langlands parameter
• The wave front set correspondence for dual pairs with one member compact
• Raising nilpotent orbits in wave-front sets