Decomposed Levi subgroups in BD-covers of classical groups

2025/09/29 by Wen-Wei Li, Li, Wen-Wei
Mathematics · #22E50 (Primary) 11F70 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2509.24571

openalex publication_date 2025/09/29 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

For finite topological central extensions of p-adic classical groups, Heiermann and Wu introduced the notion of decomposed Levi subgroups in their study of intertwining algebras. In this note, we show that for symplectic and special orthogonal groups over local fields, except the split SO(4), all Levi subgroups are decomposed if the central extension arises from the Brylinski-Deligne construction. Discussions for certain unitary groups, SO(4) and GSpin(2n+1) are also given.

Citations

• Intertwining Algebras and Affine Hecke Algebras for Finite Central Extensions of Classical p-adic Groups with Application to Metaplectic Groups
• Field change for the Cassels-Tate pairing and applications to class groups
• Twisted doubling integrals for Brylinski-Deligne extensions of classical groups
• L-groups and the Langlands program for covering groups: a historical introduction
• L-groups and parameters for covering groups
• The Langlands-Weissman Program for Brylinski-Deligne extensions
• Covers of tori over local and global fields
• Covering groups and their integral models
• Opérateurs d'entrelacement et algèbres de Hecke avec paramètres d'un groupe réductif p-adique - le cas des groupes classiques

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