# Central Characters and Conjugacy Classes in the Symmetric Group

3 POLKA - Polynomials, Combinatorics, Arithmetic
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : This article addresses several conjectures due to Jacob Katriel concerning conjugacy classes of $\S{n}$. The first conjecture expresses, for a fixed partition $\r$ of the form $r1^{n-r}$, the eigenvalues (or central characters) $\eo\r\l$ in terms of contents of $\l$. While Katriel conjectured a generic form and an algorithm to compute missing coefficients, we provide an explicit expression. The second conjecture (presented at FPSAC'98 in Toronto) gives a general form for the expression of a conjugacy class in terms of \emph{elementary} operators. We prove it using a convenient description by differential operators acting on symmetric polynomials. To conclude, we partially extend our results on $\eo\r\l$ to arbitrary partitions $\r$.
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Type de document :
Communication dans un congrès
Krob, D. and Mikhalev, A.A. & Mikhalev, A.V. 12th International Conference on Formal Power Series and Algebraic Combinatorics - FPSAC'00, 2000, Moscou/Russia, Springer, pp.238-249, 2000
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https://hal.inria.fr/inria-00099194
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 08:51:38
Dernière modification le : jeudi 10 mai 2018 - 02:06:22

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• HAL Id : inria-00099194, version 1

### Citation

Alain Goupil, Dominique Poulalhon, Gilles Schaeffer. Central Characters and Conjugacy Classes in the Symmetric Group. Krob, D. and Mikhalev, A.A. & Mikhalev, A.V. 12th International Conference on Formal Power Series and Algebraic Combinatorics - FPSAC'00, 2000, Moscou/Russia, Springer, pp.238-249, 2000. 〈inria-00099194〉

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