Invariant representations of GSp(2) under tensor product with a quadratic character

2006/12/29 by Ping-Shun Chan, Chan, Ping-Shun
Mathematics · #11F70 #11F72 #11F85 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0612850

openalex publication_date 2006/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the first part of the book, we classify the automorphic representations of \rm GSp(2) which are invariant under tensor product with a given quadratic idèle class character, via the lifting of automorphic representations of twisted endoscopic groups. In the second part of the book, we classify the admissible representations of \rm GSp(2, k), k a p-adic field, which are invariant under tensor product with a given quadratic character of k^×. This classification is given in terms of twisted character identities among the admissible representations of \rm GSp(2, k) and those of its twisted endoscopic groups. The main tool which we use is the trace formula technique.

Citations

• On Euler Products and the Classification of Automorphic Representations I
• On Euler Products and the Classification of Automorphic Forms II

Related

• Endoscopic lifting of simple supercuspidal representations of unramified U(N) to GL(N)
• Twisted character of a small representation of GL(4)
• Representations of twisted tensor products
• Triple Clasp Formulas for G₂
• R--groups, elliptic representations, and parameters for GSpin groups