Tensor category arising from
the Z_2-orbifold of Heisenberg vertex operator algebra
and its applications
报告专家：杨进伟 教授（上海交通大学）
报告时间：3月24日（周二）10：30-11：30
报告地点：四川大学数学学院西303
报告摘要：
Z_2-orbifold of Heisenberg vertex operator algebra M(1)^+ was introduced by Dong and Griess in 1998. Irreducible modules of M(1)^+ were classified by Dong-Nagatomo and their extensions were studied by Abe. In this talk, we will prove the irreducible modules of untwisted type are C_1-cofinite while irreducible modules of twisted type are not. Then we determined the category of C_1-cofinite modules completely and establish its braided tensor category structure. We also determine the fusion product decompositions and show it is a rigid category.
As an application, we prove the vertex algebras M(1)^+ and L_{-1/2}(sp(2n)) form a commutant pair in the minimal W-algebra W_{-1}(sp(2n), e_{-\theta}), and decompose this minimal W-algebra and its modules as modules for the tensor product algebra M(1)^+\otimes L_{-1/2}(sp(2n)). Using these decompositions, we show the highest weight ordinary modules for L_{-1}(sp(2n)) are all irreducible and prove the semisimplicity of the category of grading-restricted generalized modules for L_{-1}(sp(2n)).
专家简介：
杨进伟，上海交通大学副教授，国家高层次青年人才（海优）。本科和硕士毕业于北京大学数学学院，师从张继平院士。2014年在罗格斯大学取得博士学位，导师为黄一知教授。主要研究领域为顶点算子代数及其表示论，张量范畴理论。在Proc. LMS, Adv. Math., Comm. Math. Phys., Trans AMS, Math. Ann., IMRN, CCM等著名期刊上发表论文三十余篇。
邀请人：任丽
