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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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.