Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A

We introduce an analogue of the bumping algorithm for affine type A, using its natural interpretation in terms of crystals. In fact, we make explicit a particular isomorphism between connected components of the crystal graphs of Fock spaces representations of U q(ŝle). This so-called "canonical" crystal isomorphism turns out to be expressible only in terms of: − Schensted’s bumping procedure, − the cyclage isomorphism defined in [8], − a new crystal isomorphism, easy to describe, acting on cylindric multipartitions. Moreover, it yields a non-recursive characterisation of the vertices of any connected component of the crystal of the Fock space.