On the Gn-module structure of the noncommutative harmonics

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:115

Article

Briand, Emmanuel¹  Rosas, Mercedes¹  Zabrocki, Mike² 

[1] Univ Seville, Seville, Spain

[2] York Univ, Toronto, ON M3J 2R7, Canada

关键词: proper multilinear polynomials;    free Lie algebra;    harmonics;    coinvariants;    symmetric functions in noncommutative variables;   

DOI  :  10.1016/j.jcta.2007.10.005

来源: Elsevier

【 摘 要 】

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 characteristic 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. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free