江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：Minimal nilpotent finite W-algebra and cuspidal module category of sp_{2n}
报告时间：2025年06月27日（周六）16:00-17:00
报告地点：Williamhill中文官网A302
报告摘要：Finite $W$ algebras can be used to study Whittaker modules over Lie algebras. Let $U_S$ be the localization of $U(\mathfrak{sp}_{2n})$ with respect to the Ore subset $S$ generated by the root vectors $X_{\epsilon_1-\epsilon_2},\dots,X_{\epsilon_1-\epsilon_n}, X_{2\epsilon_1}$. We show that the minimal nilpotent finite $W$-algebra $W(\mathfrak{sp}_{2n}, e)$ is isomorphic to the centralizer $C_{U_S}(B)$ of some subalgebra $B$ in $U_S$, and it can be identified with a tensor product factor of $U_S$. As an application, we show that the category of cuspidal $\mathfrak{sp}_{2n}$-modules is equivalent to the category of finite-dimensional modules over $W(\mathfrak{sp}_{2n}, e)$, explaining the coincidence that both of them are semi-simple.
报告人简介：刘根强，河南大学数学与统计学院教授、博士生导师。2012年在中国科学院数学与系统科学研究院获得博士学位，主要研究领域为李代数和结合代数的表示理论；在Mathematische Zeitschrift、Transformation Groups、Journal of Algebra等国际知名数学杂志发表学术论文多篇；先后主持国家自然科学基金面上项目2项、青年项目1项及河南省自然科学基金优秀青年项目等，并合作出版英文教材《Group Theory》。