HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Reports

Characters and conjugacy classes of the symmetric group

Abstract : 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
Document type :
Reports
Complete list of metadata

https://hal.inria.fr/inria-00098749
Contributor : Publications Loria Connect in order to contact the contributor
Submitted on : Tuesday, September 26, 2006 - 8:32:52 AM
Last modification on : Friday, February 4, 2022 - 3:30:26 AM
Long-term archiving on: : Friday, November 25, 2016 - 11:56:26 AM

Identifiers

  • HAL Id : inria-00098749, version 1

Collections

Citation

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⟩

Share

Metrics

Record views

107

Files downloads

261