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Room 3.08, Building 6, Gualtar Campus, University of Minho
Henrik Winther, Artic University of Norway
The Gap Phenomenon for Automorphisms of Parabolic Geometries
We consider and resolve the gap problem for global automorphisms of complex or real parabolic geometries. Concretely, the automorphism group of a parabolic geometry of type $(G, P)$ is largest for the flat model $G/P$. The symmetry dimension is maximal in this case and is equal to $\operatorname{dim} G$. We prove that the next realizable, so-called submaximal dimension of the automorphism group of a $(G, P)$ type geometry is the dimension of a (specific) maximal parabolic subgroup in G. We also discuss maximal and submaximal dimensions of the automorphism group of compact models and provide several examples. Joint work with B. Kruglikov.