Module structure on U(H) for basic Lie superalgebras

Yan-An Cai, Kaiming Zhao
2015 Toyama Math. J   unpublished
We study the category M consisting of modules whose restriction to U(H) is free of rank 1 for the basic Lie superalgebras. We show that M is not empty only for the Lie superalgebra B(0, n) = osp(1|2n). We classify the isomorphism classes of objects in M for osp(1|2n) and determine their irreducibility. This leads to a lot of new modules over osp(1|2n).