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arXiv · 1908.01337

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

Jacopo Gandini·Pierluigi Moseneder Frajria·Paolo Papi
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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 be a Borel subgroup of G. Then B acts with finitely many orbits on the variety N_2 of the nilpotent elements in g whose height is at most 2. We provide a parametrization of the B-orbits in N_2 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.

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Jacopo Gandini, Pierluigi Moseneder Frajria, Paolo Papi. 2019-08-04. Nilpotent orbits of height 2 and involutions in the affine Weyl group. https://arxiv.org/abs/1908.01337

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