Locally analytic vectors of unitary principal series of GL_2(Qp)

Details Locally analytic vectors of unitary principal series of GL_2(Qp) Locally analytic vectors of unitary principal series of GL_2(Qp)

2011-03-13

arxiv.org/abs/1103.2543v3

Mathematics

Number Theory

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Scientific paper

The p-adic local Langlands correspondence for GL2(Qp) attaches to any 2-dimensional irreducible p-adic representation V of the absolute Galois groups of Qp an admissible unitary representation Pi(V) of GL2(Qp). The unitary principal series of GL2(Qp) are those Pi(V) corresponding to trianguline representations. In this article, for p>2, using the machinery of Colmez, we determine the space of locally analytic vectors for all non-exceptional unitary principal series of GL2(Qp) by proving a conjecture of Emerton.

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