Semisimplicity of ordinary modules
for simple affine vertex operator algebras
at positive rational shifted levels
报告专家：Robert McRae 教授（清华大学）
报告时间：6月16日（周二）10：00-11：00
报告地点：国家天元数学西南中心516
报告摘要：
Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra and let $L_k(\mathfrak{g})$ be the simple affine vertex operator algebra associated to $\mathfrak{g}$ at a level $k$ such that $-h^\vee + k\in\mathbb{Q}_{>0}$, where $h^\vee$ is the dual Coxeter number of $\mathfrak{g}$. We explain how to use recent results on braided tensor categories to show that the category of $C_1$-cofinite $L_k(\mathfrak{g})-modules is a semisimple rigid braided tensor category. For certain levels, $L_k(\mathfrak{g})$ is known to be the same as the universal affine vertex operator algebra of $\mathfrak{g}$ and level $k$, so in these cases, it follows that all generalized Verma modules induced from finite-dimensional simple $\mathfrak{g}$-modules are simple, and the category of $C_1$-cofinite $L_k(\mathfrak{g})$ is equivalent to a minor modification of the tensor category of finite-dimensional $\mathfrak{g}$-modules. This makes it possible to construct many new vertex operator algebras by extending tensor products of affine vertex operator algebras associated to $\mathfrak{g}$ at different levels.
专家简介：
Robert McRae，清华大学丘成桐数学科学中心副教授，主要研究领域为顶点算子代数、张量范畴及数学物理。在Adv. Math.、Trans. Amer. Math. Soc.、Comm. Math. Phys.、Math. Z.、J. Algebra、J. Pure Appl. Algebra等国际著名期刊发表高水平学术论文20余篇。
邀请人：任丽
