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.
The Bruhat order on abelian ideals of Borel subalgebras
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abstract
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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Nilpotent orbits of height 2 and involutions in the affine Weyl group
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.