On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~V
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 13-34
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{TIMM_2010_16_2_a1,
author = {V. A. Belonogov},
title = {On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n${.~V}},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {13--34},
publisher = {mathdoc},
volume = {16},
number = {2},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a1/}
}
TY - JOUR AU - V. A. Belonogov TI - On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~V JO - Trudy Instituta matematiki i mehaniki PY - 2010 SP - 13 EP - 34 VL - 16 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a1/ LA - ru ID - TIMM_2010_16_2_a1 ER -
%0 Journal Article %A V. A. Belonogov %T On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~V %J Trudy Instituta matematiki i mehaniki %D 2010 %P 13-34 %V 16 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a1/ %G ru %F TIMM_2010_16_2_a1
V. A. Belonogov. On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$.~V. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 13-34. http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a1/