The ladder crystal

Details The ladder crystal The ladder crystal

2009-01-22

arxiv.org/abs/0901.3565v3

Electronic Journal of Combinatorics, Volume 17 (1), 2010

Mathematics

Combinatorics

Scientific paper

n this paper I introduce a new description of the crystal $B(\Lambda_0)$ of $\hat{\mathfrak{sl}_\ell}$. As in the Misra-Miwa model of $B(\Lambda_0)$, the nodes of this crystal are indexed by partitions and the $i$-arrows correspond to adding a box of residue $i$. I then show that the two models are equivalent by interpreting the operation of regularization introduced by James as a crystal isomorphism.

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