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On irreducible characters of the group S n that are semiproportional on A n or S n \A n . VI

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Abstract

The conjecture that the alternating groups A n have no pairs of semiproportional irreducible characters is a corollary of a more general Hypothesis A, which is formulated in terms of pairs χ α and χ β of irreducible characters of the symmetric group S n that are semiproportional on one of the sets A n or S n \A n (here, α and β are the partitions of the number n corresponding to these characters). The investigation of the case h α11 ≠h β11 , 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.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    V. A. Belonogov

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  1. V. A. Belonogov
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Correspondence to V. A. Belonogov.

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Original Russian Text © V.A. Belonogov, 2010, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Vol. 16, No. 3.

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Belonogov, V.A. On irreducible characters of the group S n that are semiproportional on A n or S n \A n . VI. Proc. Steklov Inst. Math. 272 (Suppl 1), 14–35 (2011). https://doi.org/10.1134/S0081543811020027

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  • DOI: https://doi.org/10.1134/S0081543811020027

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