The canonical crystal isomorphism in Fock spaces

Thomas Gerber (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

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.

Mots clés: quantum groups; crystal graph; Robinson-Schensted; Ariki-Koike algebra

Domaines: Théorie des représentations [math.RT]

Thomas Gerber. The canonical crystal isomorphism in Fock spaces. 2013. ⟨hal-00911791v1⟩