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Journal of Mathematical Sciences

, Volume 174, Issue 1, pp 15–18 | Cite as

Polynomiality of irreducible characters of the symmetric groups

  • E. E. Goryachko
Article

Consider Young diagrams differing only by the length of the first row (i.e., the shape of diagrams below the first row is fixed). We prove that the values of the irreducible characters of the groups S n corresponding to these diagrams are given by a polynomial of a special form with respect to natural parameters related to the cycle notation of permutations. Bibliography: 3 titles.

Keywords

Russia Special Form Symmetric Group Young Diagram Mathematical Institute 
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References

  1. 1.
    W. Fulton, Young Tableaux: With Application to Representation Theory and Geometry, Cambridge Univ. Press, Cambridge (1997).zbMATHGoogle Scholar
  2. 2.
    E. E. Goryachko and F. V. Petrov, “Indecomposable characters of the group of rational rearrangements of the segment,” J. Math. Sci., 174, No. 1, 7–14 (2011).CrossRefGoogle Scholar
  3. 3.
    I. G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford (1979).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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