The canonical crystal isomorphism in Fock spaces
Résumé
We introduce an analogue of Schensted's algorithm for affine type A, using its natural interpretation in terms of crystals. In fact, we make explicit a particular crystal graph isomorphism between connected components of Fock spaces representations of U_q(sl^_e). This so-called "canonical" crystal isomorphism turns out to be expressible only in terms of: − Schensted's bumping procedure, − the cyclage isomorphism defined in [9], − a new crystal isomorphism acting on cylindric multipartitions.
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