论文标题
左扎津 - 卢斯蒂格经营者（量子）共同学和k理论
Left Demazure-Lusztig operators on equivariant (quantum) cohomology and K theory
论文作者
论文摘要
我们研究了由左旗歧管上的左乘法$ g/p $引起的苏唑 - 卢斯蒂格运营商。我们证明它们分别在任何部分旗帜歧管中生成了舒伯特细胞的Chern-Schwartz-Macpherson类（分别在eproivariant的同胞学中）（在等效的Chern阶段（In Equivariant K理论）。在此过程中，我们宣传了左右分隔的许多属性，这是共同体和K理论中的差异操作员及其对舒伯特课程的行为。我们将其应用于模棱两可的量子共同体中的左分隔差算子，以及量量子k理论，生成舒伯特类，并满足与量子产品兼容的莱布尼兹规则。
We study the Demazure-Lusztig operators induced by the left multiplication on partial flag manifolds $G/P$. We prove that they generate the Chern-Schwartz-MacPherson classes of Schubert cells (in equivariant cohomology), respectively their motivic Chern classes (in equivariant K theory), in any partial flag manifold. Along the way we advertise many properties of the left and right divided difference operators in cohomology and K theory, and their actions on Schubert classes. We apply this to construct left divided difference operators in equivariant quantum cohomology, and equivariant quantum K theory, generating Schubert classes, and satisfying a Leibniz rule compatible with the quantum product.
