Geodesic
On orbits of order ideals of minuscule posets
Journal of Algebraic Combinatorics, Tome 37 (2013) no. 3, pp. 545-569.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : a
Keywords: order ideals, antichains, minuscule posets, minuscule representations, fully commutative elements, cyclic sieving phenomenon, panyushev complement, rowmotion 
@article{JAC_2013__37_3_a1,
     author = {Rush, David B. and Shi, XiaoLin},
     title = {On orbits of order ideals of minuscule posets},
     journal = {Journal of Algebraic Combinatorics},
     pages = {545--569},
     publisher = {mathdoc},
     volume = {37},
     number = {3},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2013__37_3_a1/}
}
TY  - JOUR
AU  - Rush, David B.
AU  - Shi, XiaoLin
TI  - On orbits of order ideals of minuscule posets
JO  - Journal of Algebraic Combinatorics
PY  - 2013
SP  - 545
EP  - 569
VL  - 37
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2013__37_3_a1/
LA  - en
ID  - JAC_2013__37_3_a1
ER  - 
%0 Journal Article
%A Rush, David B.
%A Shi, XiaoLin
%T On orbits of order ideals of minuscule posets
%J Journal of Algebraic Combinatorics
%D 2013
%P 545-569
%V 37
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2013__37_3_a1/
%G en
%F JAC_2013__37_3_a1
Rush, David B.; Shi, XiaoLin. On orbits of order ideals of minuscule posets. Journal of Algebraic Combinatorics, Tome 37 (2013) no. 3, pp. 545-569. http://geodesic.mathdoc.fr/item/JAC_2013__37_3_a1/