Cyclic Characters of Alternating Groups

We determine the decomposition of cyclic characters of alternating groups into irreducible characters. As an application, we characterize pairs $(w, V)$, where w∈ Aₙ and V is an irreducible representation of Aₙ such that w admits a non-zero invariant vector in V. We also establish new global conjugacy classes for alternating groups, thereby giving a new proof of a result of Heide and Zalessky on the existence of such classes.