论文标题
K理论soergel双模型
K-theory Soergel Bimodules
论文作者
论文摘要
我们启动了K理论的soergel双模型 - A K理论的经典soergel双模型的类似物。经典的soergel双模模量可以看作是其新的K理论类似物的完整且无限的版本。我们表明，K理论的soergel双模型的形态可以用bott-samelson品种之间的高度k理论对应来描述。因此，我们从模棱两可的相干滑轮上获得了K理论soergel双模型的自然分类。我们介绍了具有仿射分层的品种上分层的k-动物的形式主义，这是伯恩斯坦 - 兰特斯衍生派生类别的k主理论类似物。我们表明，可以用K理论soergel双模型的链络合物来描述，在国旗品种上分层的圆环 - 量相位k-动物可以描述。此外，我们提出了有关标志品种和量子k理论萨克克的近似/单粒子koszul双重性的猜想。
We initiate the study of K-theory Soergel bimodules-a K-theory analog of classical Soergel bimodules. Classical Soergel bimodules can be seen as a completed and infinitesimal version of their new K-theoretic analog. We show that morphisms of K-theory Soergel bimodules can be described geometrically in terms of equivariant K-theoretic correspondences between Bott-Samelson varieties. We thereby obtain a natural categorification of K-theory Soergel bimodules in terms of equivariant coherent sheaves. We introduce a formalism of stratified equivariant K-motives on varieties with an affine stratification, which is a K-theoretric analog of the equivariant derived category of Bernstein-Lunts. We show that Bruhat-stratified torus-equivariant K-motives on flag varieties can be described in terms of chain complexes of K-theory Soergel bimodules. Moreover, we propose conjectures regarding an equivariant/monodromic Koszul duality for flag varieties and the quantum K-theoretic Satake.
