量子差分方程II的求解：三维镜像对称
Pursuing quantum difference equations II: 3D-mirror symmetry
摘要：
考虑一对关于3D镜像对称的对偶辛簇。椭圆对偶界面的K-理论极限是乘积的等变K-理论类。我们发现，这类提供了对应的产品映射的K-理论稳定的信封的K-理论稳定的信封。这种构造允许我们推广各种表示论对象对K（X）的作用，如量子群、量子外尔群、R-矩阵等的作用，到他们的行动的K-理论的各种对偶X。特别地，我们将墙R-矩阵与对偶簇的R-矩阵联系起来。作为一个例子，我们将所得结果应用于复平面上n点的Hilbert格式.在这种情况下，我们到达E.Gorsky和A. Negut的插图。
英文摘要：
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.
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