Crystal isomorphisms for irreducible highest weight U_{v}{\hat{sl}}_{e})-modules of higher level

Details Crystal isomorphisms for irreducible highest weight U_{v}{\hat{sl}}_{e})-modules of higher level Crystal isomorphisms for irreducible highest weight U_{v}{\hat{sl}}_{e})-modules of higher level

2007-06-05

arxiv.org/abs/0706.0680v2

Algebras and Representation Theory 13 (2010) 467-489

Mathematics

Representation Theory

the revised version correct minor errors

Scientific paper

We study the crystal graphs of irreducible $U_{v}(\hat{sl}}_{e})$-modules of higher level l. Generalizing works of the first author, we obtain a simple description of the bijections between the classes of multipartitions which naturally label these graphs: the Uglov multipartitions. This is achieved by expliciting an embedding of the $U_{v}(\hat{sl}}_{e})$-crystals of level l into $U_{v}(\hat{sl}_{\infty})$-crystals associated to highest weight modules.

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