Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables

被引：0

作者：

Bergeron, Francois ^{[1
]}

Lauve, Aaron ^{[2
]}

机构：

[1] Univ Quebec, LaCIM, Montreal, PQ H3C 3P8, Canada

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2010年 / 17卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

HOPF-ALGEBRAS; NONCOMMUTING VARIABLES; PARTITIONS; STATISTICS; NUMBERS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze the structure of the algebra K < x >(Gn) of symmetric polynomials in non-commuting variables in so far as it relates to K[x](Gn), its commutative counterpart. Using the "place-action" of the symmetric group, we are able to realize the latter as the in variant polynomials inside the former. We discover a tensor product decomposition of K < x >(Gn) analogous to the classical theorems of Chevalley, Shephard-Todd on finite reflection groups.

引用

页数：17