  In contrast to the classical and semiclassical settings, the Coxeter element
(12...n) which cycles the columns of an mxn matrix does not determine an
automorphism of the quantum grassmannian. Here, we show that this cycling can
be obtained by defining 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...n); we view this as a quantum analogue of the
recent result of Knutson, Lam and Speyer that the Lusztig strata of the
classical grassmannian are permuted by (12...n).
