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Math & Stats Algebra & Geometry Seminar
Tuesday, October 8th, 2024

Time: 3:30 p.m.  Place: Jeffery Hall, Room 422

Speaker: Khoa Nguyen (³ÉÈË´óƬ)

Title: On U(h)-free modules over sl(m|n)

Abstract: The study of modules over Lie algebras and superalgebras is usually divided into different categories. The first important category is the category of weight modules. In particular, such a category consists of modules that decompose into direct sums of their weight space with respect to a fixed Cartan subalgebra h. Free U(h)-modules are important non-weight modules. Such modules are free of finite rank when restricted to the Cartan subalgebra h. In this talk, I will provide the classification of U(h)-free modules of rank 2 over sl(m|1). I will also give an explicit family of weight modules of multiplicity 2 over sl(m|1) obtained from those U(h)-free modules. This is based on a joint work with Ivan Dimitrov.