On the automorphisms of hyperplane sections of generalized Grassmannians
L Manivel, V Benedetti�- Transformation Groups, 2024 - Springer
L Manivel, V Benedetti
Transformation Groups, 2024•SpringerGiven 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�…
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�…
Abstract
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 G2.
Springer