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.
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页数：17
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