Branching rules for principal series representations of unramified U(1,1)

2025/11/09 by Ekta Tiwari, Tiwari, Ekta
Mathematics · #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2511.06435

openalex publication_date 2025/11/09 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

Let G denote the unramified quasi-split unitary group \mathbbU(1,1)(F) over a p-adic field F with residual characteristic p ≠ 2. In this paper, we first construct a large family of irreducible representations of the maximal compact subgroup K = \mathbbU(1,1)(O_F) of G. We then describe the branching rules for all principal series representations of G upon restriction to K in terms of these representations. The resulting decomposition is multiplicity-free and is characterized by distinct degrees. Finally, we present two important applications of this decomposition that address certain recent open conjectures in the literature. This is the first in a series of two articles in which we provide branching rules for all irreducible smooth representations of the G upon restriction to K.

Citations

• Branching rules for irreducible depth-zero supercuspidal representations of SL(2,F), when F has residual characteristic 2
• An inductive approach to representations of general linear groups over compact discrete valuation rings
• On the unramified principal series of GL(3) over non-archimedean local\n fields
• Restriction de la repr 'esentation de Weil `a un sous-groupe compact\n maximal ou `a un tore maximal elliptique
• Branching rules for unramified principal series representations of GL(3) over a p-adic field

Related

• Branching rules for irreducible supercuspidal representations of unramified U(1,1)
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• Branching of unitary \O(1,n+1)-representations with\n non-trivial ( mathfrakg,K)-cohomology
• On certain Iwahori representations of unramified U(2, 1) in characteristic p
• Branching rules for ramified principal series representations of GL(3) over a p-adic field