# A kicking basis for the two column Garsia-Haiman modules

Abstract : In the early 1990s, Garsia and Haiman conjectured that the dimension of the Garsia-Haiman module $R_{\mu}$ is $n!$, and they showed that the resolution of this conjecture implies the Macdonald Positivity Conjecture. Haiman proved these conjectures in 2001 using algebraic geometry, but the question remains to find an explicit basis for $R_{\mu}$ which would give a simple proof of the dimension. Using the theory of Orbit Harmonics developed by Garsia and Haiman, we present a "kicking basis" for $R_{\mu}$ when $\mu$ has two columns.
Keywords :
Type de document :
Communication dans un congrès
Krattenthaler, Christian and Strehl, Volker and Kauers, Manuel. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), pp.103-114, 2009, DMTCS Proceedings
Domaine :

Littérature citée [16 références]

https://hal.inria.fr/hal-01185424
Contributeur : Coordination Episciences Iam <>
Soumis le : jeudi 20 août 2015 - 11:09:04
Dernière modification le : mardi 7 mars 2017 - 15:04:05
Document(s) archivé(s) le : mercredi 26 avril 2017 - 09:54:41

### Fichier

dmAK0109.pdf
Fichiers éditeurs autorisés sur une archive ouverte

### Identifiants

• HAL Id : hal-01185424, version 1

### Citation

Sami Assaf, Adriano Garsia. A kicking basis for the two column Garsia-Haiman modules. Krattenthaler, Christian and Strehl, Volker and Kauers, Manuel. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), pp.103-114, 2009, DMTCS Proceedings. 〈hal-01185424〉

### Métriques

Consultations de la notice

## 42

Téléchargements de fichiers