论文标题
$ k $ - 理论转移的组合Hopf代数
Shifted combinatorial Hopf algebras from $K$-theory
论文作者
论文摘要
在与刘易斯的先前联合合作中，我们开发了一种丰富的集合价值$ p $ - 分区的理论，以构建$ k $ - 峰值准对称函数的HOPF代数的理论概括。在这里，我们将此对象放在六个Hopf代数的图中，提供了$ K $ $ K $ - 理论组合的Hopf代数的转移版本，由Lam和Pylyavskyy研究。这使我们可以描述新的$ k $ - 经典峰值代数的理论类似物。我们还研究了Ikeda和Naruse的$ K $ - 理论Schur $ P $ - 和$ Q $ functions以及它们的双重函数以及它们的二元组产生的HOPF代数。在此过程中，我们得出了几种产品，coproduct和Antipode公式，并概述了许多开放问题和猜想。
In prior joint work with Lewis, we developed a theory of enriched set-valued $P$-partitions to construct a $K$-theoretic generalization of the Hopf algebra of peak quasisymmetric functions. Here, we situate this object in a diagram of six Hopf algebras, providing a shifted version of the diagram of $K$-theoretic combinatorial Hopf algebras studied by Lam and Pylyavskyy. This allows us to describe new $K$-theoretic analogues of the classical peak algebra. We also study the Hopf algebras generated by Ikeda and Naruse's $K$-theoretic Schur $P$- and $Q$-functions, as well as their duals. Along the way, we derive several product, coproduct, and antipode formulas and outline a number of open problems and conjectures.
