论文标题
全旗品种的3D镜子对称性
3d mirror symmetry of the cotangent bundle of the full flag variety
论文作者
论文摘要
Aganagic和Okounkov证明了椭圆形稳定的包膜为Quiver品种的枚举不变性提供了极点取消矩阵，称为VERTEX函数。这将$ Q $ -Difference方程的系统转换为$ \ boldsymbol {z} $ holomorphic holomorphic in $ \ boldsymbol {a} $，以$ \ boldsymbol {a} $ in $ \ boldsymbol {a} $ in $ \ baldsymbol in $ \ boldsymbol {z} $ {z} $。预计所得的功能将是3D镜双重品种的顶点函数。在本文中，我们证明，对于完整标志品种的cotangent捆绑包，以这种方式获得的功能在交换参数$ \ boldsymbol {a} \ leftrightArrow \ boldsymbol \ boldsymbol {z} $下恢复了同一品种的顶点函数。作为推论，我们推断出椭圆稳定信封的预期3D镜面关系。
Aganagic and Okounkov proved that the elliptic stable envelope provides the pole cancellation matrix for the enumerative invariants of quiver varieties known as vertex functions. This transforms a basis of a system of $q$-difference equations holomorphic in $\boldsymbol{z}$ with poles in $\boldsymbol{a}$ to a basis of solutions holomorphic in $\boldsymbol{a}$ with poles in $\boldsymbol{z}$. The resulting functions are expected to be the vertex functions of the 3d mirror dual variety. In this paper, we prove that for the cotangent bundle of the full flag variety, the functions obtained in this way recover the vertex functions for the same variety under an exchange of the parameters $\boldsymbol{a} \leftrightarrow \boldsymbol{z}$. As a corollary of this, we deduce the expected 3d mirror relationship for the elliptic stable envelope.
