One-class genera of exceptional groups over number fields

Kirschmer, Markus

Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 3, pp. 847-857.

We show that exceptional algebraic groups over number fields do not admit one-class genera of parahoric groups, except in the case $G_2$. For the group $G_2$, we enumerate all such one-class genera for the usual seven-dimensional representation.

Nous montrons que les groupes algébriques exceptionnels sur un corps de nombres n’admettent pas de genres de groupes parahoriques à une seule classe, sauf dans le cas de $G_2$. Pour le groupe $G_2$, nous énumérons tous les genres à une seule classe pour la représentation usuelle en dimension 7.

Classification: 20G30, 20G41
Keywords: Class numbers, exceptional groups

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