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On irreducible characters of the group S n that are semiproportional on A n or S N ∖ A n . I

  • Algebra and Topology
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Abstract

The hypothesis that the alternating groups A n have no pairs of semiproportional irreducible characters is reduced to a hypothesis concerning the problem of describing the pairs of irreducible characters of the symmetric group S n that are semiproportional on one of the sets A n or S n ∖ A n . The form of this hypothesis (in contrast to the form of the original one) is maximally adapted for an inductive proof. Properties of a pair of the mentioned characters are expressed in terms of the structure of Young’s diagrams for these characters. The theorem proved in this paper refines the structure of these diagrams in one of the two possible cases.

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References

  1. A. V. Belonogov, Sibirsk. Mat. Zh. 45(5), 977 (2004).

    MATH  MathSciNet  Google Scholar 

  2. A. V. Belonogov, Sibirsk. Mat. Zh. 46(2), 299 (2005).

    MATH  MathSciNet  Google Scholar 

  3. A. V. Belonogov, Algebra Logika 46(1), 3 (2007).

    MATH  MathSciNet  Google Scholar 

  4. A. V. Belonogov, Algebra Logika 47(2), 135 (2008).

    MATH  MathSciNet  Google Scholar 

  5. V. A. Belonogov, Trudy Inst. Mat. Mekh. UrO RAN 13(3), 30 (2007); English transl.: Proc. Steklov Inst. Math., Suppl. 1, 24 (2008).

    Google Scholar 

  6. V. A. Belonogov, Trudy Inst. Mat. Mekh. UrO RAN 13(1), 11 (2007); English transl.: Proc. Steklov Inst. Math., Suppl. 1, 10 (2007).

    Google Scholar 

  7. V. A. Belonogov, Trudy Inst. Mat. Mekh. UrO RAN 13(2), 13 (2007); English transl.: Proc. Steklov Inst. Math., Suppl. 2, 12 (2007).

    Google Scholar 

  8. A. V. Belonogov, Representations and Characters in the Theory of Finite Groups (UrO AN SSSR, Sverdlovsk, 1990) [in Russian].

    MATH  Google Scholar 

  9. G. James and A. Kerber, The Representation Theory of the Symmetric Group (Addison-Wesley, London, 1981).

    MATH  Google Scholar 

  10. G. James, The Representation Theory of Symmetric Groups (Mir, Moscow, 1982) [in Russian].

    MATH  Google Scholar 

  11. A. V. Belonogov, Algebra Logika 44(1), 24 (2005).

    MATH  MathSciNet  Google Scholar 

  12. A. V. Belonogov, Algebra Logika 44(6), 643 (2005).

    MATH  MathSciNet  Google Scholar 

  13. A. V. Belonogov, Sibirsk. Mat. Zh. 49(5), 992 (2008).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russia

    V. A. Belonogov

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  1. V. A. Belonogov
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Original Russian Text © V.A. Belonogov, 2008, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2008, Vol. 14, No. 2.

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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 . I . Proc. Steklov Inst. Math. 263 (Suppl 2), 150–171 (2008). https://doi.org/10.1134/S008154380806014X

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  • DOI: https://doi.org/10.1134/S008154380806014X

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