Irreducible characters of the group S n that are semiproportional on A n |
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Authors: | V. A. Belonogov |
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Affiliation: | (1) Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia |
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Abstract: | 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 α and β be partitions of a number n such that their corresponding characters χα and χβ in the group Sn are semiproportional on An. Then one of the partitions α or β is self-associated. Here, we describe all pairs (α, β) of partitions satisfying the hypothesis and the conclusion of the latter conjecture. Supported by RFBR (grant No. 07-01-00148) and by RFBR-NSFC (grant No. 05-01-39000). __________ Translated from Algebra i Logika, Vol. 47, No. 2, pp. 135–156, March–April, 2008. |
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Keywords: | alternating group irreducible character semiproportional characters |
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