On the local doubling γ-factor for classical groups over function fields

2020/03/01 by Hirotaka Kakuhama, Kakuhama, Hirotaka
Mathematics · #11F70 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2003.00469

openalex publication_date 2020/03/01 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a precise definition of an analytic γ-factor of an irreducible representation of a classical group over a local function field of odd characteristic so that it satisfies some notable properties which are enough to define it uniquely. We use the doubling method to define the γ-factor, and the main theorem extends works of Lapid-Rallis, Gan, Yamana, and the author to a classical group over a local function field of odd characteristic.

Related

• Multiplicity one theorems for the generalized doubling method
• Stability of the local gamma factor in the unitary case
• The Doubling Method in Algebraic Families
• Stability of local gamma factors arising from the doubling method for general spin groups
• Gamma-functions of representations and lifting