This article is cited in 11 papers

Irreducible characters with equal roots in the groups $S_n$ and $A_n$

V. A. Belonogov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: We show that treating of (non-trivial) pairs of irreducible characters of the group $S_n$ sharing the same set of roots on one of the sets $A_n$ and $S_n\setminus A_n$ is divided into three parts. This, in particular, implies that any pair of such characters $\chi^\alpha$ and $\chi^\beta$ ($\alpha$ and $\beta$ are respective partitions of a number $n$) possesses the following property: lengths $d(\alpha)$ and $d(\beta)$ of principal diagonals of Young diagrams for $\alpha$ and $\beta$ differ by at most 1.

Keywords: group, irreducible character, Young diagram.

UDC: 512.54

Received: 02.03.2006

 English version: Algebra and Logic, 2007, 46:1, 1–15

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