论文标题
追求量子差方程II：3D MIRROR对称性
Pursuing quantum difference equations II: 3D-mirror symmetry
论文作者
论文摘要
考虑一对相对于3D摩尔对称性双重的符号品种。椭圆双重性接口的K理论极限是产品的k理论类。我们表明，该类提供了映射K理论稳定信封的产品中的对应关系，以Keyetic稳定信封。这种构建使我们能够将各种表示理论对象在k（x）上的作用扩展，例如量子基团，量子Weyl基团，r-matrices等的作用，并将其对X的K理论的作用与X的作用。我们将壁r-matrices与双重品种的R-Matrices联系起来。 例如，我们将结果应用于复杂平面中N点的Hilbert方案。在这种情况下，我们达到了e.gorsky和A.negut的猜想。
Consider a pair of symplectic varieties dual with respect to 3D-mirror symmetry. The K-theoretic limit of the elliptic duality interface is an equivariant K-theory class of the product. We show that this class provides correspondences in the product mapping the K-theoretic stable envelopes to the K-theoretic stable envelopes. This construction allows us to extend the action of various representation theoretic objects on K(X), such as action of quantum groups, quantum Weyl groups, R-matrices etc., to their action on the K-theory of the variety dual to X. In particular, we relate the wall R-matrices to the R-matrices of the dual variety. As an example, we apply our results to the Hilbert scheme of n points in the complex plane. In this case we arrive at the conjectures of E.Gorsky and A.Negut.
