On the Action of the Restricted Weyl Group
on the Set of Orbits a Minimal Parabolic Subgroup
V. S. Zhgoona,b,* and F. Knopc,**
a Federal Scientific Center Science Research Institute
of System Studies, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia
c Friedrich Alexander University, Erlangen–Nurnberg, Germany
Correspondence to: *e-mail: zhgoon@mail.ru
Correspondence to: **e-mail: friedrich.knop@fau.de
Received 16 October, 2019
Abstract—We construct the action of the restricted Weyl group on the set of principal families of orbits of a minimal parabolic subgroup over an algebraically nonclosed field. Additionally, we relate this action to the action on a polarized cotangent bundle. These results generalize the corresponding results of Knop on the action of the Weyl group on the families of Borel orbits of maximal complexity and rank.
Keywords: reductive group actions over algebraically nonclosed fields, Weyl group, orbits of minimal parabolic subgroup, cotangent bundle
DOI: 10.1134/S1064562420010093