Locally analytic vectors of unitary principal series of GL 2(ℚp)

Ruochuan Liu; Bingyong Xie; Yuancao Zhang

doi:10.24033/asens.2163

Locally analytic vectors of unitary principal series of GL ₂(ℚ_p)

Ruochuan Liu^*
, Bingyong Xie
, Yuancao Zhang

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	167-190
Number of pages	24
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	45
Issue number	1
DOIs	https://doi.org/10.24033/asens.2163
State	Published - 2012

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

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

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Locally analytic vectors of unitary principal series of GL ₂(ℚ_p)

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