A kicking basis for the two column Garsia-Haiman modules - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2009

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.
Fichier principal
Vignette du fichier
dmAK0109.pdf (130.73 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01185424 , version 1 (20-08-2015)

Identifiers

Cite

Sami Assaf, Adriano Garsia. A kicking basis for the two column Garsia-Haiman modules. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.103-114, ⟨10.46298/dmtcs.2732⟩. ⟨hal-01185424⟩

Collections

INSMI TDS-MACS
45 View
493 Download

Altmetric

Share

Gmail Facebook X LinkedIn More