Caractères semi-simples de G 2 (F), F corps local non archimédien  [ Semi-simple characters of G 2 (F), F a local non archimedean field ]
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 6, p. 985-1025

Let F be a local non archimedean field of residual characteristic different from 2 and 3. We define semisimple strata and semisimple characters for the exceptional group G 2 (F), using the analogous objects for the group SO (8,F), the triality automorphisms and a Glauberman correspondence. We then construct the associated semisimple types and give sufficient conditions for those types to induce irreducibly, thus obtaining supercuspidal representations of the group G 2 (F).

Soit F un corps local non archimédien de caractéristique résiduelle différente de 2 et 3. Nous définissons strates semi-simples et caractères semi-simples pour le groupe exceptionnel G 2 (F) à l’aide des objets analogues pour le groupe SO (8,F), des automorphismes de trialité et d’une correspondance de Glauberman. Nous construisons alors les types semi-simples associés et nous donnons des conditions suffisantes pour que ces types s’induisent irréductiblement, obtenant ainsi des représentations supercuspidales du groupe G 2 (F).

DOI : https://doi.org/10.24033/asens.2182
Classification:  22E50
Keywords: octonions, triality, exceptional reductive group, smooth representation, semisimple character, semisimple type
@article{ASENS_2012_4_45_6_985_0,
     author = {Blasco, Laure and Blondel, Corinne},
     title = {Caract\`eres semi-simples de ${\mathrm {G}\_2}(F)$, $F$ corps local non archim\'edien},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {4e s{\'e}rie, 45},
     number = {6},
     year = {2012},
     pages = {985-1025},
     doi = {10.24033/asens.2182},
     zbl = {1271.22014},
     language = {fr},
     url = {http://www.numdam.org/item/ASENS_2012_4_45_6_985_0}
}
Blasco, Laure; Blondel, Corinne. Caractères semi-simples de ${\mathrm {G}_2}(F)$, $F$ corps local non archimédien. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 6, pp. 985-1025. doi : 10.24033/asens.2182. http://www.numdam.org/item/ASENS_2012_4_45_6_985_0/

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