论文标题
$ t^*gr（k，n）$的符号双重性
Symplectic Duality of $T^*Gr(k,n)$
论文作者
论文摘要
在本文中，我们探讨了在枚举几何形状的环境中的符号二元性（也称为3D镜子对称性）的结果。准梦的理论使人们可以将称为顶点函数的超几何功能与颤动品种相关联。在本文中，我们证明了一个公式，该公式将$ t^*gr（k，n）$的顶点函数及其符号双重偶性关联。在证明过程中，我们研究了一个$ Q $ - 差异运营商的家庭，这些家族对麦克唐纳多项式的对角线作用。我们的结果可以从组合角度解释为为$ Q $ -SELBERG类型积分提供评估公式。
In this paper, we explore a consequence of symplectic duality (also known as 3d mirror symmetry) in the setting of enumerative geometry. The theory of quasimaps allows one to associate hypergeometric functions called vertex functions to quiver varieties. In this paper, we prove a formula which relates the vertex functions of $T^*Gr(k,n)$ and its symplectic dual. In the course of the proof, we study a family of $q$-difference operators which act diagonally on Macdonald polynomials. Our results may be interpreted from a combinatorial perspective as providing an evaluation formula for a $q$-Selberg type integral.
