Non Vanishing Conjugacy Classes for an Irreducible Character of $S_{n}$

M. Purificaç\ ao Coelho and M. Antónia Duffner

Abstract: An irreducible character of the symmetric group $S_{n}$ is a triangular character if it is associated to a partition of the form $(m,m-1,...,2,1)$. We prove that an irreducible character $\chi$ is triangular if and only if it vanishes on all conjugacy classes whose cycle decomposition contains at least one transposition.\Prgrf Furthermore if the character $\chi$ is not triangular and $\chi\ne[2,2]$, there is a class where a transposition and a cycle of length one occur, for which $\chi$ does not vanish.

Full text of the article:

• Compressed PostScript file (60 kilobytes)
• PDF file (120 kilobytes)