On the local theta representation

2014/08/04 by Chunhui Wang, Wang, Chun-Hui
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Mathematical Analysis and Transform Methods #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1408.0625

openalex publication_date 2014/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the algebraic framework in which one can define, in the manner of the theta correspondence, a correspondence between representations of two locally profinite groups H₁, H₂. In particular, we examine when and how such a correspondence can be extended to bigger groups G₁, G₂ containing H₁, H₂ respectively as normal subgroups. As an application, we discuss the theta correspondence for a reductive dual pair of the similitude groups in the non-archimedean case.

Related

• Lectures on local theta correspondence
• Theta correspondence for symplectic-orthogonal and metaplectic-orthogonal p-adic dual pairs
• Coincidence of algebraic and smooth theta correspondences
• Theta correspondence via group C*-algebras
• The ℓ-modular local theta correspondence