Journal of Lie Theory 28 (2018), No. 2, 443--477
Copyright Heldermann Verlag 2018
Sous-Groupes Réductifs Canoniques des Sous-Groupes Biparaboliques de SO(n, C) ou SO(p, q) dont l'Algèbre de Lie est Quasi-Réductive
Nabila Djebali
Dép. Mathématiques et Applications, Faculté des Sciences de Tunis, Université Tunis El Manar, 2092 Tunis, Tunisie
nabila.djebali@math.univ-poitiers.fr
We associate a not necessarily unique meander graph to each biparabolic subgroup of SO(n, C) and SO(p, q). In terms of the associated meander graph to a biparabolic subgroup, we give a necessary and sufficient condition for its Lie algebra to be quasi-reductive, describe in this case the conjugacy classes of its canonical reductive subgroups and determine when it admits discrete series.
Keywords: Quasireductive Lie algebras, biparabolic subgroups, meander graphs.
MSC: 17B45, 17B20, 22E60
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