Mikhail V. Ignatev - Gradedness of the set of rook placements in An−1

cm:9535 - Communications in Mathematics, July 15, 2021, Volume 29 (2021), Issue 2 (Special Issue: 3rd International Workshop on Nonassociative Algebras in Málaga) - https://doi.org/10.2478/cm-2021-0016
Gradedness of the set of rook placements in An−1

Authors: 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.


Volume: Volume 29 (2021), Issue 2 (Special Issue: 3rd International Workshop on Nonassociative Algebras in Málaga)
Published on: July 15, 2021
Imported on: May 11, 2022
Keywords: General Mathematics,[MATH]Mathematics [math]


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