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, p. 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 ).
Received : 2014-06-10
Revised : 2015-02-18
Accepted : 2015-06-11
Published online : 2016-07-28
Classification:  22E50,  11F80,  11F85
Keywords: Supersingular representations, unitary group, mod-p representations
@article{AIF_2016__66_4_1545_0,
     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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {4},
     year = {2016},
     pages = {1545-1582},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2016__66_4_1545_0}
}
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. https://aif.centre-mersenne.org/item/AIF_2016__66_4_1545_0/

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