no. 4
A Classification of the Irreducible mod-p Representations of U(1,1)(ℚ p 2 /ℚ p )
Kozioł, Karol1
1 University of Toronto Department of Mathematics 40 St. George Street, Room 6290 Toronto, ON, M5S 2E4 (Canada)
Annales de l'Institut Fourier, Volume 66 (2016) no. 4, pp. 1545-1582

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 ).

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 ).

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3043
Classification: 22E50, 11F80, 11F85
Keywords: Supersingular representations, unitary group, mod-$p$ representations
Mots-clés : Représentations supersingulières, groupe unitaire, représentations modulo $p$

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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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, Volume 66 (2016) no. 4, pp. 1545-1582. doi: 10.5802/aif.3043

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