On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. VI

V. A. Belonogov

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 25-44

Résumé

The conjecture that the alternating groups $A_n$ have no pairs of semiproportional irreducible characters is a corollary of a more general conjecture A, formulated in terms of pairs $\chi^\alpha$ and $\chi^\beta$ of irreducible characters of the symmetric group $S_n$ that are semiproportional on one of the sets $A_n$ or $S_n\setminus A_n$ (here $\alpha$ and $\beta$ are partitions of the number n corresponding to these characters). In the paper the investigation of the case is begun in which $h^\alpha_{11}\ne h^\beta_{11}$, i.e. (1, 1)-hooks of the Young diagrams of the partitions $\alpha$ и $\beta$ have different lengths.

Détail

Keywords: symmetric groups, alternating groups, irreducible characters, semiproportionality.

Bibliographie

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[2] Belonogov V. A., “O neprivodimykh kharakterakh gruppy $S_n$, poluproportsionalnykh na $A_n$ ili na $S_n\setminus A_n$. II”, Tr. In-ta matematiki i mekhaniki UrO RAN, 14, no. 3, 2008, 58–68

[3] Belonogov V. A., “O neprivodimykh kharakterakh gruppy $S_n$, poluproportsionalnykh na $A_n$ ili na $S_n\setminus A_n$. III”, Tr. In-ta matematiki i mekhaniki UrO RAN, 14, no. 4, 2008, 12–30

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