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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Volume 16, Number 3, Pages 25–44
(Mi timm573)
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This article is cited in 1 scientific paper (total in 1 paper)
On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. VI
V. A. Belonogov Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
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.
Keywords:
symmetric groups, alternating groups, irreducible characters, semiproportionality.
Received: 18.06.2010
Citation:
V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. VI”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 3, 2010, 25–44; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S14–S35
Linking options:
https://www.mathnet.ru/eng/timm573 https://www.mathnet.ru/eng/timm/v16/i3/p25
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Abstract page: | 254 | Full-text PDF : | 63 | References: | 38 | First page: | 2 |
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