On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~VI
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 25-44
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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.
@article{TIMM_2010_16_3_a2,
author = {V. A. Belonogov},
title = {On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n${.~VI}},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {25--44},
publisher = {mathdoc},
volume = {16},
number = {3},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a2/}
}
TY - JOUR AU - V. A. Belonogov TI - On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~VI JO - Trudy Instituta matematiki i mehaniki PY - 2010 SP - 25 EP - 44 VL - 16 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a2/ LA - ru ID - TIMM_2010_16_3_a2 ER -
%0 Journal Article %A V. A. Belonogov %T On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~VI %J Trudy Instituta matematiki i mehaniki %D 2010 %P 25-44 %V 16 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a2/ %G ru %F TIMM_2010_16_3_a2
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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 25-44. http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a2/