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Reports Year : 1999

Characters and conjugacy classes of the symmetric group


This article addresses several conjectures due to Jacob Katriel concerning conjugacy classes of $\S{n}$ viewed as operators acting by multiplication. 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 $\r$. || Nous démontrons plusieurs conjectures dues à Jacob Katriel qui portent sur les classes de conjugaisons de $\S{n}$ vues comme opérateurs agissant par multiplication. La première conjecture exprime, pour une partition fixée $\rho$ de la forme $r1^{n-r}$, le
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Dates and versions

inria-00098749 , version 1 (26-09-2006)


  • HAL Id : inria-00098749 , version 1


Alain Goupil, Dominique Poulalhon, Gilles Schaeffer. Characters and conjugacy classes of the symmetric group. [Intern report] 99-R-349 || goupil99a, 1999, 12 p. ⟨inria-00098749⟩
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