A Classification of the Irreducible mod-p Representations of U(1,1)( p 2 / p )
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)( p 2 / p ) in two variables. We then investigate Langlands parameters in characteristic p associated to U(1,1)( p 2 / p ), and propose a correspondence between certain equivalence classes of Langlands parameters and certain isomorphism classes of semisimple L-packets on U(1,1)( p 2 / p ).

Soit p un nombre premier. Nous classifions les représentations lisses irréductibles modulo p du groupe unitaire non-ramifié U(1,1)( p 2 / p ) en deux variables. Ensuite, nous étudions les paramètres de Langlands en caractéristique p associés à U(1,1)( p 2 / 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)( p 2 / p ).

Published online:
DOI: 10.5802/aif.3043
Classification: 22E50,  11F80,  11F85
Keywords: Supersingular representations, unitary group, mod-p representations
     author = {Kozio{\l}, Karol},
     title = {A {Classification} of the {Irreducible} mod-$p$ {Representations} of $\textnormal{U}(1,1)(\mathbb{Q}_{p^2}/\mathbb{Q}_p)$},
     journal = {Annales de l'Institut Fourier},
     pages = {1545--1582},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {66},
     number = {4},
     year = {2016},
     doi = {10.5802/aif.3043},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3043/}
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.3043/

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