Darboux transformations for the strict KP hierarchy

We introduce the notion of Darboux transformations for the strict KP hierarchy. We previously showed that solutions of this integrable hierarchy can be constructed from a flag variety $\mathcal{F}(1)$. Here, we describe which two points in this flag variety are connected by such a transformation. Moreover, we present a closed form of the operators that realize this transformation and describe their geometric characteristics. We show which of these Darboux transformations map solutions of the strict $n$-KdV hierarchy to other solutions of this reduction of the strict KP hierarchy.