Geodesic
On the action of the restricted Weyl group on the set of orbits a minimal parabolic subgroup
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 29-34

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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. 
@article{DANMA_2020_490_a6,
     author = {V. S. Zhgoon and F. Knop},
     title = {On the action of the restricted {Weyl} group on the set of orbits a minimal parabolic subgroup},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {29--34},
     publisher = {mathdoc},
     volume = {490},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_490_a6/}
}
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V. S. Zhgoon; F. Knop. On the action of the restricted Weyl group on the set of orbits a minimal parabolic subgroup. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 29-34. http://geodesic.mathdoc.fr/item/DANMA_2020_490_a6/