Geodesic
On Automorphisms with Natural Tangent Actions on Homogeneous Parabolic Geometries
Jan Gregorovic1 ; Lenka Zalabová2
1Department of Mathematics, Aarhus University, Ny Munkegade 118, Aarhus C 8000, Denmark
2Institute of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia, Branisovská 31, Ceské Budejovice 370 05, Czech Republic
Journal of Lie Theory, Tome 25 (2015) no. 3, pp. 677-715

Voir la notice de l'article provenant de la source Heldermann Verlag

We consider automorphisms of homogeneous parabolic geometries with a fixed point. Parabolic geometries carry the distinguished distributions and we study those automorphisms which enjoy natural actions on the distributions at the fixed points. We describe the sets of such automorphisms on homogeneous parabolic geometries in detail and classify whether there are non-flat homogeneous parabolic geometries carrying such automorphisms. We present two general constructions of such geometries and we provide complete classifications for the types (G,P) of the parabolic geometries that have G simple and the automorphisms are of order 2.
Classification : 53C10, 53C30, 58J70
Mots-clés : Parabolic geometries, homogeneous spaces, automorphisms with fixed points, harmonic curvature restrictions

Jan Gregorovic  1   ; Lenka Zalabová  2

1 Department of Mathematics, Aarhus University, Ny Munkegade 118, Aarhus C 8000, Denmark
2 Institute of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia, Branisovská 31, Ceské Budejovice 370 05, Czech Republic 
Jan Gregorovic; Lenka Zalabová. On Automorphisms with Natural Tangent Actions on Homogeneous Parabolic Geometries. Journal of Lie Theory, Tome 25 (2015) no. 3, pp. 677-715. http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a2/
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     author = {Jan Gregorovic and Lenka Zalabov\'a},
     title = {On {Automorphisms} with {Natural} {Tangent} {Actions} on {Homogeneous} {Parabolic} {Geometries}},
     journal = {Journal of Lie Theory},
     pages = {677--715},
     year = {2015},
     volume = {25},
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     url = {http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a2/}
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