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 Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 2, Pages 13–34 (Mi timm546)

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

V. A. Belonogov

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

Abstract: Investigations are continued concerning the conjecture that the alternating groups $A_n$ have no pairs of semiproportional irreducible characters. In order to prove this conjecture by induction on $n$, the author earlier proposed a new conjecture, 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 set $A_n$ or $S_n\setminus A_n$ ($\alpha$ and $\beta$ are partitions of the number n corresponding to these characters). The theorem proved in this paper allows one to exclude from consideration the item of this conjecture in which the 4-kernels of the partitions $\alpha$ and $\beta$ have type $3^k.2.\Sigma_l$.

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

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UDC: 512.54

Citation: V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. V”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 2, 2010, 13–34

Citation in format AMSBIB
\Bibitem{Bel10} \by V.~A.~Belonogov \paper On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~V \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2010 \vol 16 \issue 2 \pages 13--34 \mathnet{http://mi.mathnet.ru/timm546} \elib{http://elibrary.ru/item.asp?id=14809435} 

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This publication is cited in the following articles:
1. V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. VI”, Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S14–S35
2. V. A. Belonogov, “O neprivodimykh kharakterakh gruppy $S_n$, poluproportsionalnykh na $A_n$ ili na $S_n\setminus A_n$. VII”, Tr. IMM UrO RAN, 17, no. 1, 2011, 3–16
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