Geodesic
Crystal graphs of irreducible $\mathcal{U}_v (\widehat{\mathfrak{sl}}_e)$-modules of level two and Uglov bipartitions
Journal of Algebraic Combinatorics, Tome 27 (2008) no. 2, pp. 143-162.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We give a simple description of the natural bijection between the set of FLOTW bipartitions and the set of Uglov bipartitions (which generalizes the set of Kleshchev bipartitions). These bipartitions, which label the crystal graphs of irreducible $U _{ v}([^(\mathfrak sl)] _{ e})$ mathcalU_v(widehatmathfraksl_e) -modules of level two, naturally appear in the context of the modular representation theory of Hecke algebras of type $B _{ n }$.
Classification : 17B37, 20C08
Keywords: keywords Hecke algebras, modular representations, canonical basis, crystal graph 
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     author = {Jacon, Nicolas},
     title = {Crystal graphs of irreducible $\mathcal{U}_v (\widehat{\mathfrak{sl}}_e)$-modules of level two and {Uglov} bipartitions},
     journal = {Journal of Algebraic Combinatorics},
     pages = {143--162},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2008__27_2_a6/}
}
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Jacon, Nicolas. Crystal graphs of irreducible $\mathcal{U}_v (\widehat{\mathfrak{sl}}_e)$-modules of level two and Uglov bipartitions. Journal of Algebraic Combinatorics, Tome 27 (2008) no. 2, pp. 143-162. http://geodesic.mathdoc.fr/item/JAC_2008__27_2_a6/