Geodesic
Irreducible characters with equal roots in the groups $S_n$ and $A_n$
Algebra i logika, Tome 46 (2007) no. 1, pp. 3-25

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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.
Mots-clés : group
Keywords: irreducible character, Young diagram. 
@article{AL_2007_46_1_a0,
     author = {V. A. Belonogov},
     title = {Irreducible characters with equal roots in the groups $S_n$ and~$A_n$},
     journal = {Algebra i logika},
     pages = {3--25},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_1_a0/}
}
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V. A. Belonogov. Irreducible characters with equal roots in the groups $S_n$ and $A_n$. Algebra i logika, Tome 46 (2007) no. 1, pp. 3-25. http://geodesic.mathdoc.fr/item/AL_2007_46_1_a0/