Blocks for mod p representations of GL₂(Q_p)

2011/04/29 by Paskunas, Vytautas · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1104.5602

Abstract

Let π₁ and π₂ be absolutely irreducible smooth representations of G=GL₂(Q_p) with a central character, defined over a finite field of characteristic p. We show that if there exists a non-split extension between π₁ and π₂ then they both appear as subquotients of the reduction modulo p of a unit ball in a crystalline Banach space representation of G. The results of Berger-Breuil describe such reductions and allow us to organize the irreducible representation into blocks. The result is new for p=2, the proof, which works for all p, is new.

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