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The Bruhat order on abelian ideals of Borel subalgebras

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arxiv 1806.08622 v3 pith:H4T47AV6 submitted 2018-06-22 math.AG math.RT

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keywords abelianborelalgebraalgebraicalgebraicallyb-orbitsb-stablebruhat
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Let G be a quasi simple algebraic group over an algebraically closed field k whose characteristic is not very bad for G, and let B be a Borel subgroup of G with Lie algebra b. Given a B-stable abelian subalgebra a of the nilradical of b, we parametrize the B-orbits in a and we describe their closure relations.

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

    math.AG 2019-08 conditional novelty 6.0 of 10

    The inclusion order on Borel orbits in the height-2 nilpotent locus of an almost simple group matches the Bruhat order on affine Weyl group involutions attached to strongly orthogonal root sets.

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