eng
episciences.org
Communications in Mathematics
1804-1388
2336-1298
2021-07-15
Volume 29 (2021), Issue 2...
10.2478/cm-2021-0016
9535
journal article
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.
https://cm.episciences.org/9535/pdf
General Mathematics
[MATH]Mathematics [math]