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
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2009
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2732
- Akses
- Open Access ✓