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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - V. S. Zhgoon
AU  - F. Knop
TI  - On the action of the restricted Weyl group on the set of orbits a minimal parabolic subgroup
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 29
EP  - 34
VL  - 490
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2020_490_a6/
LA  - ru
ID  - DANMA_2020_490_a6
ER  - 
%0 Journal Article
%A V. S. Zhgoon
%A F. Knop
%T On the action of the restricted Weyl group on the set of orbits a minimal parabolic subgroup
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2020
%P 29-34
%V 490
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2020_490_a6/
%G ru
%F DANMA_2020_490_a6
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/

[1] Knop F., “On the set of orbits for a Borel subgroup”, Commentarii Mathematici Helvetici, 70:1 (1995), 285–309 | DOI | MR | Zbl

[2] Springer T.A., Linear algebraic groups, Springer Science Business Media, 2010 | MR

[3] Platonov V., Rapinchuk A., Algebraic Groups and Number Theory, Pure and Applied Mathematics, 139, 1st Ed., Academic Press, 1993 | MR

[4] Zhgun V.S., Knop F., “Slozhnost deistviya reduktivnykh grupp nad algebraicheski nezamknutym polem i silnaya stabilnost deistvii na flagovykh mnogoobraziyakh”, DAN, 485:1 (2019), 22–26 | Zbl

[5] Vinberg E.B., “Slozhnost deistvii reduktivnykh grupp”, Funkts. analiz i ego pril., 20:1 (1986), 1–13 | MR | Zbl

[6] Knop F., Krotz B., Reductive group actions, 2016, arXiv: 1604.01005

[7] Brion M., “Quelques proprietes des espaces homogenes spheriques”, Manuscripta Math., 55:2 (1986), 191–198 | DOI | MR | Zbl

[8] Borel A., Tits J., “Groupes reductifs”, Inst. Hautes Etudes Sci. Publ. Math., 27 (1965), 55–150 | DOI | MR

[9] Kempf G., “Instability in invariant theory”, Ann. Math., 108:2 (1978), 299–316 | DOI | MR | Zbl

[10] Knop F., “The asymptotic behavior of invariant collective motion”, Inventiones mathematicae, 116:1 (1994), 309–328 | DOI | MR | Zbl

[11] Popov V.L., Vinberg E.B., “Invariant theory”, Algebraic geometry. IV, Encyclopedia Math. Sci., 55, Springer-Verlag, B.–Heidelberg–N.Y., 1994, 123–278 | DOI