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Article Dans Une Revue Transformation Groups Année : 2022

On the automorphisms of hyperplane sections of generalized Grassmannians

Résumé

Given a smooth hyperplane section H of a rational homogeneous space G/P with Picard number one, we address the question whether it is always possible to lift an automorphism of H to the Lie group G, or more precisely to Aut(G/P). Using linear spaces and quadrics in H, we show that the answer is positive up to a few well understood exceptions related to Jordan algebras. When G/P is an adjoint variety, we show how to describe Aut(H) completely, extending results obtained by Prokhorov and Zaidenberg when G is the exceptional group G_2.
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Dates et versions

hal-03360605 , version 1 (30-09-2021)

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Vladimiro Benedetti, Laurent Manivel. On the automorphisms of hyperplane sections of generalized Grassmannians. Transformation Groups, 2022, ⟨10.1007/s00031-022-09757-1⟩. ⟨hal-03360605⟩
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