  The problem of finding Schur-positive sets of permutations, originally posed
by Gessel and Reutenauer, has seen some recent developments. Schur-positive
sets of pattern-avoiding permutations have been found by Sagan et al and a
general construction based on geometric operations on grid classes has been
given by the authors. In this paper we prove that horizontal rotations of
Schur-positive subsets of permutations are always Schur-positive. The proof
applies a cyclic action on standard Young tableaux of certain skew shapes and a
jeu-de-taquin type straightening algorithm. As a consequence of the proof we
obtain a notion of cyclic descent set on these tableaux, which is rotated by
the cyclic action on them.
