On some crystalline representations of $GL_2(Q_p)$

Vytautas Paskunas

Published 2008-04-11, updated 2009-02-09Version 2

We show that the universal unitary completion of certain locally algebraic representation of $G:=\GL_2(\Qp)$ with $p>2$ is non-zero, topologically irreducible, admissible and corresponds to a 2-dimensional crystalline representation with non-semisimple Frobenius via the $p$-adic Langlands correspondence for $G$.