Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B ⊂ G be a Borel subgroup. Then B acts with finitely many orbits on the variety N2 ⊂ g of the nilpotent elements whose height is at most 2. We provide a parametrization of the B-orbits in N2 in terms of subsets of pairwise orthogonal roots, and we provide a complete description of the inclusion order among the B-orbit closures in terms of the Bruhat order on certain involutions in the affine Weyl group of g.

Nilpotent orbits of height 2 and involutions in the affine Weyl group

Gandini, Jacopo;
2020

Abstract

Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B ⊂ G be a Borel subgroup. Then B acts with finitely many orbits on the variety N2 ⊂ g of the nilpotent elements whose height is at most 2. We provide a parametrization of the B-orbits in N2 in terms of subsets of pairwise orthogonal roots, and we provide a complete description of the inclusion order among the B-orbit closures in terms of the Bruhat order on certain involutions in the affine Weyl group of g.
Gandini, Jacopo; Möseneder Frajria, Pierluigi; Papi, Paolo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/759054
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