由斯托克斯现象产生的量子群表示
Representations of quantum groups arising from the Stokes phenomenon
AI总结：
该研究证明二阶极点处量子微分方程的量子斯托克斯矩阵可生成量子群$U_q(\frak{gl}_n)$的表示，建立了斯托克斯现象与量子群理论的对应，并提出向典型李代数及任意阶极点推广的方向。
摘要：
本文证明了二阶极点处量子微分方程的量子斯托克斯矩阵可生成量子群$U_q(\frak{gl}_n)$的表示。我们从二阶极点处经典斯托克斯矩阵的形变量子化视角阐释了研究结果。由此，我们能得到斯托克斯现象理论与量子群理论之间的对应字典。本文简要讨论了若干此类对应关系，并概述了将研究结果推广至所有典型李代数以及任意阶极点处量子微分方程的思路。
英文摘要：
In this paper we prove that the quantum Stokes matrices of the quantum differential equation at a second order pole give rise to representations of the quantum group $U_q(\frak{gl}_n)$. We explain our results from the viewpoint of deformation quantization of the classical Stokes matrices at a second order pole. As a consequence, we can get a dictionary between the theory of Stokes phenomenon and the theory of quantum groups. We briefly discuss several such correspondences, and outline the generalization of our results to all classical types of Lie algebras and to the quantum differential equation at an arbitrary order pole.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
