论文标题
在超空间中非公共对称函数的HOPF代数上
On the Hopf algebra of noncommutative symmetric functions in superspace
论文作者
论文摘要
我们详细研究了由Fishel，Lapointe和Pinto引入的Superspace Snsym中非公共对称函数的HOPF代数。我们介绍了SNSYM的原始元素家族，并将非交通性基本和功率总和函数扩展到超空间。然后，我们给出有关这些功能系列的公式。此外，我们在超空间中引入了非交通性的色带Schur功能，并为其产品提供了明确的公式。我们表明，这些功能的双重基础是由Superspace中所谓基本的准对称函数的家族给出的。这使我们能够获得一个明确的公式，用于超空间中基本的准对称函数的相关。此外，通过在超空间中投影非交通性的色带Schur函数，我们为超空间中对称函数代数定义了新的基础。另一方面，我们还表明，Snsym可以实现为树木的霍夫代数。
We study in detail the Hopf algebra of noncommutative symmetric functions in superspace sNSym, introduced by Fishel, Lapointe and Pinto. We introduce a family of primitive elements of sNSym and extend the noncommutative elementary and power sum functions to superspace. Then, we give formulas relating these families of functions. Also, we introduce noncommutative Ribbon Schur functions in superspace and provide a explicit formula for their product. We show that the dual basis of these function is given by a family of the so--called fundamental quasisymmetric functions in superspace. This allows us to obtain a explicit formula for the coproduct of fundamental quasisymmetric functions in superspace. Additionally, by projecting the noncommutative Ribbon Schur functions in superspace, we define a new basis for the algebra of symmetric functions in superspace. On the other hand, we also show that sNSym can be realised as a Hopf algebra of trees.
