Geodesic
Partition models for the crystal of the basic $U_{q}(\widehat {\mathfrak{sl}}_{n})$-module
Journal of Algebraic Combinatorics, Tome 32 (2010) no. 3, pp. 339-370.

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Summary: For each $n \geq 3$, we construct an uncountable family of models of the crystal of the basic $U _{ q}([^(\mathfrak sl)] _{ n})$ U_q($\widehat {\mathfrak $sl_n)-module. These models are all based on partitions, and include the usual $n$-regular and $n$-restricted models, as well as Berg's ladder crystal, as special cases.
Keywords: keywords partition, highest-weight crystal 
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     author = {Fayers, Matthew},
     title = {Partition models for the crystal of the basic $U_{q}(\widehat {\mathfrak{sl}}_{n})$-module},
     journal = {Journal of Algebraic Combinatorics},
     pages = {339--370},
     publisher = {mathdoc},
     volume = {32},
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     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__32_3_a6/}
}
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Fayers, Matthew. Partition models for the crystal of the basic $U_{q}(\widehat {\mathfrak{sl}}_{n})$-module. Journal of Algebraic Combinatorics, Tome 32 (2010) no. 3, pp. 339-370. http://geodesic.mathdoc.fr/item/JAC_2010__32_3_a6/