DOAJ Open Access 2009

A kicking basis for the two column Garsia-Haiman modules

Sami Assaf Adriano Garsia

Abstrak

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.

Topik & Kata Kunci

Penulis (2)

S

Sami Assaf

A

Adriano Garsia

Format Sitasi

Assaf, S., Garsia, A. (2009). A kicking basis for the two column Garsia-Haiman modules. https://doi.org/10.46298/dmtcs.2732

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2732
Informasi Jurnal
Tahun Terbit
2009
Sumber Database
DOAJ
DOI
10.46298/dmtcs.2732
Akses
Open Access ✓