Cyclic Sieving, Promotion, and Representation Theory

Abstract : We prove a collection of conjectures due to Abuzzahab-Korson-Li-Meyer, Reiner, and White regarding the cyclic sieving phenomenon as it applies to jeu-de-taquin promotion on rectangular tableaux. To do this, we use Kazhdan-Lusztig theory and a characterization of the dual canonical basis of $\mathbb{C}[x_{11}, \ldots , x_{nn}]$ due to Skandera. Afterwards, we extend our results to analyzing the fixed points of a dihedral action on rectangular tableaux generated by promotion and evacuation, suggesting a possible sieving phenomenon for dihedral groups. Finally, we give applications of this theory to cyclic sieving phenomena involving reduced words for the long elements of hyperoctohedral groups, handshake patterns, and noncrossing partitions.
Type de document :
Communication dans un congrès
Krattenthaler, Christian and Sagan, Bruce. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), pp.393-410, 2008, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [21 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01185133
Contributeur : Coordination Episciences Iam <>
Soumis le : mercredi 19 août 2015 - 11:40:35
Dernière modification le : jeudi 11 mai 2017 - 01:02:52
Document(s) archivé(s) le : vendredi 20 novembre 2015 - 10:25:42

Fichier

dmAJ0134.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01185133, version 1

Collections

Citation

Brendon Rhoades. Cyclic Sieving, Promotion, and Representation Theory. Krattenthaler, Christian and Sagan, Bruce. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), pp.393-410, 2008, DMTCS Proceedings. 〈hal-01185133〉

Partager

Métriques

Consultations de la notice

28

Téléchargements de fichiers

67