Representations lisses de GL(m,D), IV : representations supercuspidales

2006/07/12 by Vincent Sécherre, Secherre, Vincent, Shaun Stevens +1 · 1 citation
Mathematics · #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0607298

openalex publication_date 2006/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a non Archimedean locally compact field and let D be a central F-division algebra. We prove that any positive level supercuspidal irreducible representation of the group GL(m,D) is compactly induced from a representation of a compact mod center open subgroup of GL(m,D). More precisely, we prove that such representations contain a maximal simple type.

Cited by

• An introduction to representations of p-adic groups

Related

• On the types for supercuspidal representations of inner forms of GL_N
• Progrès récents sur les représentations supercuspidales
• Comparison of types for inner forms of GL_N
• Comparing Bushnell-Kutzko and Sécherre's constructions of types for GL_N and its inner forms with Yu's construction
• Supercuspidal support of irreducible modulo l-representations of SL_n(F)