Skew characters and cyclic sieving

Abstract In 2010, Rhoades proved that promotion on rectangular standard Young tableaux, together with the associated fake-degree polynomial, provides an instance of cyclic sieving phenomenon. We extend this result to m -tuples skew tableaux same shape, for fixed , subject condition th power polynomial evaluates nonnegative integers at roots unity. However, we are unable specify explicit group action. Put differently, determine in which cases tensor a character symmetric carries permutation representation group. To do so, use method proposed by Amini and first author, amounts establishing bound number border-strip shape. Finally, apply our results invariant theory powers adjoint general linear particular, prove existence bijection between permutations Stembridge’s alternating intertwines rotation promotion.