Generalized Whittaker functions and Jacquet modules

2020/09/03 by Matringe, Nadir
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2009.01624

Abstract

Let G be a reductive group over a non archimedean local field, and ψ a non-degenerate character of the unipotent radical U₀ of a minimal parabolic subgroup P₀=M₀U₀. For P=MU⊇ P₀, we show that the descent to the Jacquet module J_P(W(G,ψ)) of Delorme's constant term map from the space W(G,ψ) of generalized Whittaker functions on G to W(M,ψ_{|U0∩ M}) is the dual map of the inverse of the isomorphism of Bushnell and Henniart from J_P^-(W_c(G,ψ^-1)) to W_c(M,ψ_{|U0∩ M}^-1) (in particular the constant term map is surjective). We give applications of this result. We also provide an integral version of Lapid and Mao's asymptotic expansion for integral generalized Whittaker functions in the context of ℓ-adic representations.

Related

• Derivatives and Asymptotics of Whittaker functions
• Derivatives and asymptotics of Whittaker functions
• Measuring the Space of Metaplectic Whittaker Functions
• Algorithms for parabolic inductions and Jacquet modules in GL_n
• Generalized Whittaker models beyond \mathfraksl₂-triples