Crystal-like structures arising from the dKP hierarchy
Abstract1+1 dimensional time evolutions obtained from the discrete KP hierarchy can be re-interpreted as certain types of Yang-Baxter maps. As these maps are known to be related to geometric crystals, it seems natural to ask whether such crystals also arise within the context of the dKP hierarchy. It will be shown that this is indeed the case and that a particular class of Darboux transformations for the linear problem of the dKP hiearchy gives rise to crystal-like structures.
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