Geodesic
The ladder crystal
The electronic journal of combinatorics, Tome 17 (2010)
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In 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.
DOI : 10.37236/369
Classification : 05E10, 17B37, 20C08
Mots-clés : crystal bases, partitions, crystal isomorphisms, operations on ladders 
@article{10_37236_369,
     author = {Chris Berg},
     title = {The ladder crystal},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/369},
     zbl = {1288.05295},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/369/}
}
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Chris Berg. The ladder crystal. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/369

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