Twisting the quantum grassmannian

In contrast to the classical and semiclassical settings, the Coxeter element $(12\dots n)$ which cycles the columns of an $m\times n$ matrix does not determine an automorphism of the quantum grassmannian. Here, we show that this cycling can be obtained by means of a cocycle twist. A consequence is that the torus invariant prime ideals of the quantum grassmannian are permuted by the action of the Coxeter element $(12\dots n)$. We view this as a quantum analogue of the recent result of Knutson, Lam and Speyer, where the Lusztig strata of the classical grassmannian are permuted by $(12\dots n)$.