Gradedness of the set of rook placements in A n - 1

Mikhail V. Ignatev

Communications in Mathematics (2021)

  • Volume: 29, Issue: 2, page 171-182
  • ISSN: 1804-1388

Abstract

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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 A n - 1 with respect to a slightly different order and prove that this poset is graded.

How to cite

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Ignatev, Mikhail V.. "Gradedness of the set of rook placements in $A_{n-1}$." Communications in Mathematics 29.2 (2021): 171-182. <http://eudml.org/doc/297726>.

@article{Ignatev2021,
abstract = {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 $A_\{n-1\}$ with respect to a slightly different order and prove that this poset is graded.},
author = {Ignatev, Mikhail V.},
journal = {Communications in Mathematics},
keywords = {Root system; rook placement; Borel subgroup; coadjoint orbit; graded poset},
language = {eng},
number = {2},
pages = {171-182},
publisher = {University of Ostrava},
title = {Gradedness of the set of rook placements in $A_\{n-1\}$},
url = {http://eudml.org/doc/297726},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Ignatev, Mikhail V.
TI - Gradedness of the set of rook placements in $A_{n-1}$
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 2
SP - 171
EP - 182
AB - 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 $A_{n-1}$ with respect to a slightly different order and prove that this poset is graded.
LA - eng
KW - Root system; rook placement; Borel subgroup; coadjoint orbit; graded poset
UR - http://eudml.org/doc/297726
ER -

References

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