The ladder crystal

Abstract

n this paper I introduce a new description of the crystal $B({\Lambda }_0)$ of $\widehat{{\mathfrak{sl}}_{\ell }}$. 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.