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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

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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