论文标题
仿生草个子切片的量子微分方程
Quantum Differential Equation for Slices of the Affine Grassmannian
论文作者
论文摘要
与还原组$ \ mathbf {g} $相关的仿生草是通常的国旗品种的仿真类似物。它是泊松品种及其符号分辨率的丰富来源。这些空间是中岛Quiver品种双重锥形符号分辨率的例子。在这项工作中，我们研究了它们的量子连接。我们使用D. Maulik和A. Okounkov [Arxiv：1211.1287]的稳定信封来为此连接编写一个明确的公式。乘法的经典部分来自[arxiv：2210.09967]。纯量子部分的计算是根据A. Braverman，D。Maulik和A. Okounkov的变形方法完成的[ARXIV：1001.0056]。对于简单的$ \ Mathbf {G} $，我们确定了langlands dual dual Group $ \ mathbf {g}^\ vee $的三角knizhnik-zamolodchikov方程的量子连接。
The affine Grassmannian associated to a reductive group $\mathbf{G}$ is an affine analogue of the usual flag varieties. It is a rich source of Poisson varieties and their symplectic resolutions. These spaces are examples of conical symplectic resolutions dual to the Nakajima quiver varieties. In this work, we study their quantum connection. We use the stable envelopes of D. Maulik and A. Okounkov[arXiv:1211.1287] to write an explicit formula for this connection. The classical part of the multiplication comes from [arXiv:2210.09967]. The computation of the purely quantum part is done based on the deformation approach of A. Braverman, D. Maulik and A. Okounkov[arXiv:1001.0056]. For the case of simply-laced $\mathbf{G}$, we identify the quantum connection with the trigonometric Knizhnik-Zamolodchikov equation for the Langlands dual group $\mathbf{G}^\vee$.
