Locally analytic vectors of unitary principal series of  GL 2 ( ℚ p )

Ruochuan Liu; Bingyong Xie; Yuancao Zhang

Annales scientifiques de l'École Normale Supérieure (2012)

  • Volume: 45, Issue: 1, page 167-190
  • ISSN: 0012-9593

Abstract

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The p -adic local Langlands correspondence for  GL 2 ( ℚ p ) attaches to any 2 -dimensional irreducible p -adic representation V of  G ℚ 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  GL 2 ( ℚ p ) by proving a conjecture of Emerton.

How to cite

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Liu, Ruochuan, Xie, Bingyong, and Zhang, Yuancao. "Locally analytic vectors of unitary principal series of ${\mathrm {GL}}_2({\mathbb {Q}}_p)$." Annales scientifiques de l'École Normale Supérieure 45.1 (2012): 167-190. <http://eudml.org/doc/272161>.

@article{Liu2012,
abstract = {The $p$-adic local Langlands correspondence for $\{\mathrm \{GL\}\}_2(\{\mathbb \{Q\}\}_p)$ attaches to any $2$-dimensional irreducible $p$-adic representation $V$ of $G_\{\{\mathbb \{Q\}\}_p\}$ an admissible unitary representation $\Pi (V)$ of $\{\mathrm \{GL\}\}_2(\{\mathbb \{Q\}\}_p)$. The unitary principal series of $\{\mathrm \{GL\}\}_2(\{\mathbb \{Q\}\}_p)$ are those $\Pi (V)$ corresponding to trianguline representations. In this article, for $p&gt;2$, using the machinery of Colmez, we determine the space of locally analytic vectors $\Pi (V)_\mathrm \{an\}$ for all non-exceptional unitary principal series $\Pi (V)$ of $\{\mathrm \{GL\}\}_2(\{\mathbb \{Q\}\}_p)$ by proving a conjecture of Emerton.},
author = {Liu, Ruochuan, Xie, Bingyong, Zhang, Yuancao},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {$p$-adic local Langlands correspondence; $(\varphi ,\gamma )$-modules; trianguline representations; unitary principal series; locally analytic vectors},
language = {eng},
number = {1},
pages = {167-190},
publisher = {Société mathématique de France},
title = {Locally analytic vectors of unitary principal series of $\{\mathrm \{GL\}\}_2(\{\mathbb \{Q\}\}_p)$},
url = {http://eudml.org/doc/272161},
volume = {45},
year = {2012},
}

TY - JOUR
AU - Liu, Ruochuan
AU - Xie, Bingyong
AU - Zhang, Yuancao
TI - Locally analytic vectors of unitary principal series of ${\mathrm {GL}}_2({\mathbb {Q}}_p)$
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2012
PB - Société mathématique de France
VL - 45
IS - 1
SP - 167
EP - 190
AB - The $p$-adic local Langlands correspondence for ${\mathrm {GL}}_2({\mathbb {Q}}_p)$ attaches to any $2$-dimensional irreducible $p$-adic representation $V$ of $G_{{\mathbb {Q}}_p}$ an admissible unitary representation $\Pi (V)$ of ${\mathrm {GL}}_2({\mathbb {Q}}_p)$. The unitary principal series of ${\mathrm {GL}}_2({\mathbb {Q}}_p)$ are those $\Pi (V)$ corresponding to trianguline representations. In this article, for $p&gt;2$, using the machinery of Colmez, we determine the space of locally analytic vectors $\Pi (V)_\mathrm {an}$ for all non-exceptional unitary principal series $\Pi (V)$ of ${\mathrm {GL}}_2({\mathbb {Q}}_p)$ by proving a conjecture of Emerton.
LA - eng
KW - $p$-adic local Langlands correspondence; $(\varphi ,\gamma )$-modules; trianguline representations; unitary principal series; locally analytic vectors
UR - http://eudml.org/doc/272161
ER -

References

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