A Classification of the Irreducible mod-$p$ Representations of $\textnormal{U}(1,1)(\mathbb{Q}_{p^2}/\mathbb{Q}_p)$

Kozioł, Karol

doi:10.5802/aif.3043

A Classification of the Irreducible mod-

p

Representations of

U (1, 1) (ℚ_{p^{2}} / ℚ_{p})

[Une classification des représentations irréductibles modulo

p

U (1, 1) (ℚ_{p^{2}} / ℚ_{p})

]

Kozioł, Karol ¹

¹ University of Toronto Department of Mathematics 40 St. George Street, Room 6290 Toronto, ON, M5S 2E4 (Canada)

Annales de l'Institut Fourier, Tome 66 (2016) no. 4, pp. 1545-1582.

Résumé
Abstract

Soit $p$ un nombre premier. Nous classifions les représentations lisses irréductibles modulo $p$ du groupe unitaire non-ramifié $U (1, 1) (ℚ_{p^{2}} / ℚ_{p})$ en deux variables. Ensuite, nous étudions les paramètres de Langlands en caractéristique $p$ associés à $U (1, 1) (ℚ_{p^{2}} / ℚ_{p})$ et proposons une correspondance entre certaines classes d’équivalence de paramètres de Langlands et certaines classes d’isomorphisme de $L$ -paquets semi-simples de $U (1, 1) (ℚ_{p^{2}} / ℚ_{p})$ .

Let $p$ be a prime number. We classify all smooth irreducible mod- $p$ representations of the unramified unitary group $U (1, 1) (ℚ_{p^{2}} / ℚ_{p})$ in two variables. We then investigate Langlands parameters in characteristic $p$ associated to $U (1, 1) (ℚ_{p^{2}} / ℚ_{p})$ , and propose a correspondence between certain equivalence classes of Langlands parameters and certain isomorphism classes of semisimple $L$ -packets on $U (1, 1) (ℚ_{p^{2}} / ℚ_{p})$ .

Reçu le : 2014-06-10
Révisé le : 2015-02-18
Accepté le : 2015-06-11
Publié le : 2016-07-28

DOI : 10.5802/aif.3043

Classification : 22E50, 11F80, 11F85
Keywords: Supersingular representations, unitary group, mod-$p$ representations
Mot clés : Représentations supersingulières, groupe unitaire, représentations modulo $p$

Affiliations des auteurs :

Kozioł, Karol ¹

¹ University of Toronto Department of Mathematics 40 St. George Street, Room 6290 Toronto, ON, M5S 2E4 (Canada)

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     title = {A {Classification} of the {Irreducible} mod-$p$ {Representations} of $\textnormal{U}(1,1)(\mathbb{Q}_{p^2}/\mathbb{Q}_p)$},
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Kozioł, Karol. A Classification of the Irreducible mod-$p$ Representations of $\textnormal{U}(1,1)(\mathbb{Q}_{p^2}/\mathbb{Q}_p)$. Annales de l'Institut Fourier, Tome 66 (2016) no. 4, pp. 1545-1582. doi : 10.5802/aif.3043. https://aif.centre-mersenne.org/articles/10.5802/aif.3043/

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