Irreducible characters of the group Sn that are semiproportional on An

• Autores: V. A. Belonogov
• Localización: Algebra and logic, ISSN 0002-5232, Vol. 47, Nº. 2, 2008, págs. 77-90
• Idioma: inglés
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• Resumen

  • 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.