Antipode Formulas for some Combinatorial Hopf Algebras
Antipode Formulas for some Combinatorial Hopf Algebras
复制标题
一些组合 Hopf 代数的对极公式
DOI：
10.37236/5949
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Rebecca Patrias
中科院分区：
文献类型：
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作者：
Rebecca Patrias
受Buch关于集值表与Grassmannian k理论相关的工作的启发，Lam和Pylyavskyy研究了六个组合Hopf代数，它们可以被认为是对称函数、拟对称函数、非交换对称函数的Hopf代数和Malvenuto-Reutenauer置换Hopf代数的k -论类似物。他们描述了所有未知情况下的双代数结构，但没有找到对跖图的明确公式。我们给出了对称函数、拟对称函数和非交换对称函数的k -理论类似物的对映映射的组合公式。
Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, Lam and Pylyavskyy studied six combinatorial Hopf algebras that can be thought of as K-theoretic analogues of the Hopf algebras of symmetric functions, quasisymmetric functions, noncommutative symmetric functions, and of the Malvenuto-Reutenauer Hopf algebra of permutations. They described the bialgebra structure in all cases that were not yet known but left open the question of finding explicit formulas for the antipode maps. We give combinatorial formulas for the antipode map for the K-theoretic analogues of the symmetric functions, quasisymmetric functions, and noncommutative symmetric functions.