Gradedness of the set of rook placements in An−1

Mikhail V. Ignatev

A rook placement is a subset of a root system consisting of positive roots with pairwise non-positive inner products. To each rook placement in a root system one can assign the coadjoint orbit of the Borel subgroup of a reductive algebraic group with this root system. Degenerations of such orbits induce a natural partial order on the set of rook placements. We study combinatorial structure of the set of rook placements in An− 1 with respect to a slightly different order and prove that this poset is graded.

Domaines: Mathématiques [math]

Mikhail V. Ignatev. Gradedness of the set of rook placements in An−1. Communications in Mathematics, 2021, Volume 29 (2021), Issue 2 (Special Issue: 3rd International Workshop on Nonassociative Algebras in Málaga) (2), pp.171 - 182. ⟨10.2478/cm-2021-0016⟩. ⟨hal-03665022⟩