Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables
Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables
复制标题
DOI：
10.4153/cjm-2008-013-4
复制
发表时间：
2005-02
期刊：
影响因子：
--
通讯作者：
N. Bergeron;C. Reutenauer;M. Rosas;M. Zabrocki
中科院分区：
文献类型：
--
作者：
N. Bergeron;C. Reutenauer;M. Rosas;M. Zabrocki
摘要在非交换对称函数空间上引入一种自然的Hopf代数结构。这个代数的基由集合划分索引。我们表明，存在一个自然包含的非交换对称函数的Hopf代数在这个更大的空间。我们还认为这个代数作为一个子空间的非交换多项式，并用它来了解结构的空间的谐波和协不变关于这个集合的非交换多项式，并得出两个类似的Chevalley定理在非交换设置。
Abstract We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions. The bases for this algebra are indexed by set partitions. We show that there exists a natural inclusion of the Hopf algebra of noncommutative symmetric functions in this larger space. We also consider this algebra as a subspace of noncommutative polynomials and use it to understand the structure of the spaces of harmonics and coinvariants with respect to this collection of noncommutative polynomials and conclude two analogues of Chevalley’s theorem in the noncommutative setting.