David B. Rush ; Xiaolin Shi - On Orbits of Order Ideals of Minuscule Posets

dmtcs:12804 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12804
On Orbits of Order Ideals of Minuscule PosetsArticle

Authors: David B. Rush 1; Xiaolin Shi 1

  • 1 Department of Mathematics [MIT]

An action on order ideals of posets considered by Fon-Der-Flaass is analyzed in the case of posets arising from minuscule representations of complex simple Lie algebras. For these minuscule posets, it is shown that the Fon-Der-Flaass action exhibits the cyclic sieving phenomenon, as defined by Reiner, Stanton, and White. A uniform proof is given by investigation of a bijection due to Stembridge between order ideals of minuscule posets and fully commutative Weyl group elements. This bijection is proven to be equivariant with respect to a conjugate of the Fon-Der-Flaass action and an arbitrary Coxeter element. If $P$ is a minuscule poset, it is shown that the Fon-Der-Flaass action on order ideals of the Cartesian product $P \times [2]$ also exhibits the cyclic sieving phenomenon, only the proof is by appeal to the classification of minuscule posets and is not uniform.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: order ideals,antichains,minuscule posets,minuscule representations,fully commutative elements,cyclic sieving phenomenon,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Reflection Group Combinatorics; Funder: National Science Foundation; Code: 1001933

Consultation statistics

This page has been seen 69 times.
This article's PDF has been downloaded 57 times.