Resolutions for principal series representations of p-adic GL(n)

2014/08/15 by Rachel Ollivier, Ollivier, Rachel
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1408.3679

openalex publication_date 2014/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a nonarchimedean locally compact field with residue characteristic p and G(F) the group of F-rational points of a connected reductive group. Following Schneider and Stuhler, one can realize, in a functorial way, any smooth complex finitely generated representation of G(F) as the 0-homology of a certain coefficient system on the semi-simple building of G(F). It is known that this method does not apply in general for smooth mod p representations of G(F), even when G= GL(2). However, we prove that a principal series representation of GL(n,F) over a field with arbitrary characteristic can be realized as the 0-homology of the corresponding coefficient system.

Citations

• Modules universels de GL(3) sur un corps p-adique en caractéristique p

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