On the S_n-module structure of the noncommutative harmonics

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dc.creatorBriand, Emmanuel
dc.creatorRosas, Mercedes
dc.creatorZabrocki, Mike
dc.date2007-04-09
dc.date2007-10-02
dc.date.accessioned2026-07-07T10:12:14Z
dc.date.available2026-07-07T10:12:14Z
dc.descriptionUsing a noncommutative analog of Chevalley's decomposition of polynomials into symmetric polynomials times coinvariants due to Bergeron, Reutenauer, Rosas, and Zabrocki we compute the graded Frobenius series for their two sets of noncommutative harmonics with respect to the left action of the symmetric group (acting on variables). We use these results to derive the Frobenius series for the enveloping algebra of the derived free Lie algebra in n variables.
dc.description13 pages. Expanded version of a paper to appear in "Journal of Combinatorial Theory, series A" (http://www.elsevier.com/locate/jcta)
dc.identifierhttps://arxiv.org/abs/0704.1101
dc.identifierhttp://arxiv.org/abs/0704.1101
dc.identifierJournal of Combinatorial Theory, Series A, Volume 115, Issue 6, August 2008, pages 1077-1085.
dc.identifierdoi:10.1016/j.jcta.2007.10.005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172116
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject16W50; 05A18; 05E05
dc.titleOn the S_n-module structure of the noncommutative harmonics
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