Theta lifts and distinction for regular supercuspidal representations

2018/04/26 by Chong Zhang, Zhang, Chong
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1804.09878

openalex publication_date 2018/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article has a twofold purpose. First, by recent works of Kaletha and Loke-Ma, we give an explicit description of the local theta correspondence between regular supercuspidal representations in the equal rank symplectic-orthogonal case. Second, based on this description, we show that the local theta correspondence preserves distinction with respect to unramified Galois involutions.

Citations

• A `relative' local Langlands correspondence
• Distinguished regular supercuspidal representations

Related

• Local Theta Correspondences between Supercuspidal Representations
• Base change and theta correspondences for supercuspidal representations\n of SL(2)
• Distinction and quadratic base change for regular supercuspidal representations
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• Local theta correspondences between epipelagic supercuspidal\n representations