On the restriction of representations of \GL₂(F) to a Borel subgroup

2006/10/04 by Vytautas Paškūnas, Paskunas, Vytautas · 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/0610156

openalex publication_date 2006/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a non-Archimedean local field and let p be the residual characteristic of F. Let G=GL₂(F) and let P be a Borel subgroup of G. In this paper we study the restriction of irreducible representations of G on E-vector spaces to P, where E is an algebraically closed field of characteristic p. We show that in a certain sense P controls the representation theory of G. We then extend our results to smooth \oK[G]- modules of finite length and unitary K-Banach space representations of G, where \oK is the ring of integers of a complete discretely valued field K, with residue field E.

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• Restriction problem for mod p representations of GL₂ over a finite field

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