On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~IV.
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 12-33
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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
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 sets $A_n$ 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 $3^k.\Sigma_l$.
Keywords:
symmetric groups, alternating groups, irreducible characters, semiproportionality.
@article{TIMM_2009_15_2_a1,
author = {V. A. Belonogov},
title = {On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n${.~IV.}},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {12--33},
publisher = {mathdoc},
volume = {15},
number = {2},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a1/}
}
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%0 Journal Article %A V. A. Belonogov %T On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~IV. %J Trudy Instituta matematiki i mehaniki %D 2009 %P 12-33 %V 15 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a1/ %G ru %F TIMM_2009_15_2_a1
V. A. Belonogov. On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~IV.. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 12-33. http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a1/