Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 54, No. 4, pp. 441-447 (1997)

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

M. Purificaç\ ao Coelho and M. Antónia Duffner

Universidade de Lisboa, C.A.U.L.,
Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex - PORTUGAL

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.

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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

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