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University of Toronto
Thu 25 May 2017, 3:30pm SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Ordinary representations and locally analytic socle for GL_n(Q_p)
ESB 4127
Thu 25 May 2017, 3:30pm-4:30pm


Suppose that rho is an irreducible automorphic n-dimensional global 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 that this representation occurs globally in a space of p-adic automorphic forms cut out by rho. In work in progress we prove many new cases of this conjecture, assuming that rho is moreover crystalline with distinct Hodge-Tate weights.