Base change and theta correspondences for supercuspidal representations of SL(2)

2011/01/25 by David Manderscheid, Manderscheid, David
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1101.4862

This is a revison of a previous version of the paper. Typos have been corrected and more details of the argument have been added

openalex publication_date 2011/01/25 · arxiv created 2012/11/08 · arxiv updated 2012/11/12 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Let F be a p-adic field with p odd. Quadratic base change and theta-lifting are shown to be compatible for supercuspidal representations of SL(2,F). The argument involves the theory of types and the lattice model of the Weil representation.

Related

• Local Theta Correspondences between Supercuspidal Representations
• Theta lifts and distinction for regular supercuspidal representations
• Simple supercuspidals and the Langlands correspondence
• Theta Correspondence for U(1,1) and U(2)
• Changements de base explicites des représentations supercuspidales de U(1,1)(F)