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. 
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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/

[1] V. A. Belonogov, “O neprivodimykh kharakterakh grupp $S_n$ i $A_n$”, Sib. matem. zh., 45:5 (2004), 977–994 | MR | Zbl

[2] V. A. Belonogov, “O nulyakh v tablitsakh kharakterov grupp $S_n$ i $A_n$. II”, Algebra i logika, 44:6 (2005), 643–663 | MR | Zbl

[3] V. A. Belonogov, “O nulyakh v tablitsakh kharakterov grupp $S_n$ i $A_n$”, Algebra i logika, 44:1 (2005), 24–43 | MR | Zbl

[4] V. A. Belonogov, Predstavleniya i kharaktery v teorii konechnykh grupp, UrO AN SSSR, Sverdlovsk, 1990

[5] G. James, A. Kerber, The representation theory of the symmetric group, Addison-Wesley, London, 1981 | MR

[6] G. Dzheims, Teoriya predstavlenii simmetricheskikh grupp, Mir, M., 1982 | MR