论文标题
Yang-baxter代数，高级分区功能和$ K $ - 部分旗帜捆绑
Yang-Baxter algebra, higher rank partition functions and $K$-theoretic Gysin map for partial flag bundles
论文作者
论文摘要
我们研究了$ k $ - $ a $ a $ a部分标志捆绑的理论gysin地图，从集成性的角度来看。我们介绍了$ q = 0 $ u_q（\ wideHat {sl_n}）$ q = 0 $变性的几种类型的分区功能，这些函数在矩形网格上介绍了$ u_q（\ wideHat {sl_n}）$顶点模型，这些模型因边界条件和大小而有所不同，并且可以看作是grothendieck类别的grothendieck类别的grothendieck类别的grothendieck类别和零件的part型标志。通过得出$ q = 0 $ $ $ u_q（\ widehat {sl_n}）$ yang-baxter代数的多个换向关系，并与$ k $ - 理论的副旗的描述使用对称性操作员的部分旗帜捆绑在一起，我们显示了$ k $ - $ k $ - $ k $ - $ k $ - 理论吉斯式的界限属于一个类型的派系，即在一个类型的类型函数上，构成了一个派别，该函数是派别的，即在一个类型的类型函数上，一位零件的构图一侧从第一种类型逆转。这概括了作者从格拉曼（Grassmann）捆绑到部分旗帜束的先前结果。我们还讨论了$ k $ - 理论吉辛地图的分区功能和应用程序的不稳定版本。
We investigate the $K$-theoretic Gysin map for type $A$ partial flag bundles from the viewpoint of integrability. We introduce several types of partition functions for one version of $q=0$ degeneration of $U_q(\widehat{sl_n})$ vertex models on rectangular grids which differ by boundary conditions and sizes, and can be viewed as Grothendieck classes of the Grothendieck group of a nonsingular variety and partial flag bundles. By deriving multiple commutation relations for the $q=0$ $U_q(\widehat{sl_n})$ Yang-Baxter algebra and combining with the description of the $K$-theoretic Gysin map for partial flag bundles using symmetrizing operators, we show that the $K$-theoretic Gysin map of the first type of partition functions on a rectangular grid is given by the second type whose boundary conditions on one side are reversed from the first type. This generalizes the author's previous result from Grassmann bundles to partial flag bundles. We also discuss the inhomogenous version of the partition functions and applications to the $K$-theoretic Gysin map.
