On irreducible characters of the group Sn that are semiproportional on An or Sn\An. VI

The conjecture that the alternating groups An have no pairs of semiproportional irreducible characters is a corollary of a more general Hypothesis A, which is formulated in terms of pairs χα and χβ of irreducible characters of the symmetric group Sn that are semiproportional on one of the sets An or Sn\An (here, α and β are the partitions of the number n corresponding to these characters). The investigation of the case h11α≠h11β, i.e., when the (1, 1)-hooks of the Young diagrams of the partitions α and β have different lengths, is begun in this paper.