Crystal rules for \((\ell,0)\)-JM partitions
The electronic journal of combinatorics, Tome 17 (2010)
Vazirani and the author [Electron. J. Combin., 15 (1) (2008), R130] gave a new interpretation of what we called $\ell$-partitions, also known as $(\ell,0)$-Carter partitions. The primary interpretation of such a partition $\lambda$ is that it corresponds to a Specht module $S^{\lambda}$ which remains irreducible over the finite Hecke algebra $H_n(q)$ when $q$ is specialized to a primitive $\ell^{th}$ root of unity. To accomplish this we relied heavily on the description of such a partition in terms of its hook lengths, a condition provided by James and Mathas. In this paper, I use a new description of the crystal $reg_\ell$ which helps extend previous results to all $(\ell,0)$-JM partitions (similar to $(\ell,0)$-Carter partitions, but not necessarily $\ell$-regular), by using an analogous condition for hook lengths which was proven by work of Lyle and Fayers.
DOI :
10.37236/391
Classification :
05E10, 05A17, 20C30
Mots-clés : \(\ell\)-partitions, \((\ell,0)\)-Carter partitions, Specht module, Hecke algebra, crystal
Mots-clés : \(\ell\)-partitions, \((\ell,0)\)-Carter partitions, Specht module, Hecke algebra, crystal
@article{10_37236_391,
author = {Chris Berg},
title = {Crystal rules for {\((\ell,0)\)-JM} partitions},
journal = {The electronic journal of combinatorics},
year = {2010},
volume = {17},
doi = {10.37236/391},
zbl = {1264.05138},
url = {http://geodesic.mathdoc.fr/articles/10.37236/391/}
}
Chris Berg. Crystal rules for \((\ell,0)\)-JM partitions. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/391
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