Resumen de Irreducible characters of the group Sn that are semiproportional on An

V. A. Belonogov

• Previously, we dubbed the conjecture that the alternating group An has no semiproportional irreducible characters for any natural n [1]. This conjecture was then shown to be equivalent to the following [3]. Let ? and ? be partitions of a number n such that their corresponding characters ?? and ?? in the group Sn are semiproportional on An. Then one of the partitions ? or ? is self-associated. Here, we describe all pairs (?, ?) of partitions satisfying the hypothesis and the conclusion of the latter conjecture.