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SUMMARY:Ordinary representations and locally analytic socle for GL_n(Q_p) 
  - Florian Herzig (University of Toronto)
DTSTART:20171205T143000Z
DTEND:20171205T153000Z
UID:TALK88461@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:Suppose that rho is an irreducible automorphic n-dimensional g
 lobal p-adic Galois representation that is upper-triangular locally at p. 
 In previous work with Breuil we constructed a unitary representation of GL
 _n(Q_p) on a p-adic Banach space (depending only on rho locally at p) that
  is an extension of finitely many principal series\, and we conjectured th
 at this representation occurs globally in a space of p-adic automorphic fo
 rms cut out by rho. In work in progress we prove many new cases of this co
 njecture\, assuming that rho is moreover crystalline. 
LOCATION:MR13
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