Repr\'esentations cristallines irr\'eductibles de ${\rm GL}_2(\mathbf{Q}_p)$

Publication date: 4 October 2004

Abstract: In cite[S1.3]{Br2}, some unitary representations of

{m G L}_{2} (m a t h b f Q_{p})

on

p

-adic Banach spaces are associated to 2-dimensional irreducible crystalline representations of

. Some conjectures are formulated concerning those Banach spaces (non triviality, topological irreducibility, admissibility). We prove those conjectures by reinterpreting those Banach as spaces of functions of a certain type on

m a t h b f Q_{p}

, and then by using the theory of

(p h i, G a m m a)

-modules associated to the corresponding crystalline representations.

Mathematics Subject Classification ID

Discontinuous groups and automorphic forms (11Fxx)

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