Regular irreducible characters of a hyperspecial compact group and Weil representations over finite fields

2015/09/25 by Koichi Takase, Takase, Koichi
Mathematics · #20C25 #20C33 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1509.07573

openalex publication_date 2015/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A method to construct irreducible unitary representations of a hyperspecial compact subgroup of a reductive group over p-adic field with odd p is presented. Our method is based upon Cliffods theory and Weil representations over finite fields. It works under an assumption of the triviality of certain Schur multipliers defined for an algebraic group over a finite field. The assumption of the triviality has good evidences in the case of general linear groups and highly probable in regular cases in general. We will give several examples of classical groups where the Schur multipliers are actually trivial.

Related

• Regular irreducible characters of a hyperspecial compact group
• Restriction de la repr 'esentation de Weil `a un sous-groupe compact\n maximal ou `a un tore maximal elliptique
• Regular characters of GL_n(O) and Weil representations over finite fields
• Characterization of supercuspidal representations and very regular elements
• Weil representations and metaplectic groups over an integral domain