The minimal polynomials of powers of cycles in the ordinary representations of symmetric and alternating groups

Nanying Yang; Alexey Staroletov

paper

The minimal polynomials of powers of cycles in the ordinary representations of symmetric and alternating groups

arXiv:1911.06049

Abstract

Denote the alternating and symmetric groups of degree $n$ by $A_{n}$ and $S_{n}$ respectively. Consider a permutation $σ \in S_{n}$ all of whose nontrivial cycles are of the same length. We find the minimal polynomials of $σ$ in the ordinary irreducible representations of $A_{n}$ and $S_{n}$ .

21 pages