On the S_n-module structure of the noncommutative harmonics
Combinatorics
2008-10-23 v2 Representation Theory
Abstract
Using 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.
Keywords
Cite
@article{arxiv.0704.1101,
title = {On the S_n-module structure of the noncommutative harmonics},
author = {Emmanuel Briand and Mercedes Rosas and Mike Zabrocki},
journal= {arXiv preprint arXiv:0704.1101},
year = {2008}
}
Comments
13 pages. Expanded version of a paper to appear in "Journal of Combinatorial Theory, series A" (http://www.elsevier.com/locate/jcta)