论文标题
纯辫子小组动作O类别O模块
Pure braid group actions on category O modules
论文作者
论文摘要
令G为对称的kac-moody代数和u_h（g）其量化的包围代数。回答P. etingof的问题，我们证明了U_H（G）的量子Weyl组运营商在任何类别的o（不一定是可集成的）u_h（g）-Module V.纯辫子组的规范作用中产生了典型的作用v在g and u_h（g）的类别O类别的eTingof-kazhdan等效性下。我们还扩展了这些结果，以产生抛物线纯辫子基团的等效量子Weyl基团和抛物线核心类别O的抛物面类别O（g）和G。
Let g be a symmetrisable Kac-Moody algebra and U_h(g) its quantised enveloping algebra. Answering a question of P. Etingof, we prove that the quantum Weyl group operators of U_h(g) give rise to a canonical action of the pure braid group of g on any category O (not necessarily integrable) U_h(g)-module V. By relying on our recent results in arXiv:1512.03041, we show that this action describes the monodromy of the rational Casimir connection on the g-module corresponding to V under the Etingof-Kazhdan equivalence of category O for g and U_h(g). We also extend these results to yield equivalent quantum Weyl group and monodromic representations of parabolic pure braid groups on parabolic category O for U_h(g) and g.
