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

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.