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

^*此作品的通讯作者

数学科学学院

University of Michigan, Ann Arbor
Peking University

科研成果: 期刊稿件 › 文章 › 同行评审

18 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	167-190
页数	24
期刊	Annales Scientifiques de l'Ecole Normale Superieure
卷	45
期	1
DOI	https://doi.org/10.24033/asens.2163
出版状态	已出版 - 2012

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10.24033/asens.2163

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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(ℚp)

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