Journal of Lie Theory

no. 3
On Automorphisms with Natural Tangent Actions on Homogeneous Parabolic Geometries
Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 677-715
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.
DOI: 10.5802/jolt.855
Classification: 53C10, 53C30, 58J70
Keywords: Parabolic geometries, homogeneous spaces, automorphisms with fixed points, harmonic curvature restrictions 
@article{JOLT_2015_25_3_a2,
     author = {J. Gregorovic and L. 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},
     number = {3},
     doi = {10.5802/jolt.855},
     zbl = {1330.53033},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.855/}
}
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%A L. Zalabová
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%J Journal of Lie Theory
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J. Gregorovic; L. Zalabová. On Automorphisms with Natural Tangent Actions on Homogeneous Parabolic Geometries. Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 677-715. doi: 10.5802/jolt.855

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