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

2019/11/14 by Nanying Yang, Yang, Nanying, Alexey Staroletov +1 · 1 citation
Computer Science · Engineering · Mathematics · #20C30 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1911.06049

openalex publication_date 2019/11/14 · openalex created_date 2019/11/22 · openalex updated_date 2026/08/01

Abstract

Denote the alternating and symmetric groups of degree n by A_n and S_n respectively. Consider a permutation σ∈ 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.

Cited by

• On the Positivity of Dihedral Branching Coefficients of the Symmetric and Alternating Groups

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