The value of the global intertwining operators on spherical vectors

2017/09/26 by Volker Heiermann, Heiermann, Volker
Mathematics · #11F66 #11F70 #22E55 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1709.09107

openalex publication_date 2017/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a global field, G an unramified quasi-split reductive group over F and chi an everywhere unramified automorphic character of a maximal maximally split torus of G. Using Langlands-Shahidi theory, we compute the meromorphic function defined by the action of a global standard intertwining operator associated to chi on a spherical vector and show that the ratio of its poles in the positive Weyl chamber is well behaved.

Citations

• On the unramified spherical automorphic spectrum

Related

• Langlands parameters associated to special maximal parahoric spherical representations
• On the asymptotics of Hecke operators for reductive groups
• Residues of Intertwining Operators for Classical Groups with an Appendix "L-Functions and Poles of Intertwining Operators"
• Minimal representations: spherical vectors and automorphic functionals
• Matrix coefficients of intertwining operators and the Bruhat order