Weight Modules Of Orthosymplectic Lie Superalgebras
Abstract
A long-standing problem in representation theory is the classification of all simple weight modules of the classical Lie superalgebras. This problem was reduced to the classification of simple bounded highest weight modules. The latter classification has been accomplished for all classical Lie superalgebras except for the orthosymplectic series osp(m|2n) where m = 1, 3, 4, 5, 6. In this thesis, we complete the classification of the simple bounded highest weight modules of osp(1|2n) (i.e., for m = 1). The classification is obtained by developing constraints on primitive vectors in tensor products of bounded (Weyl) and finite-dimensional osp(1|2n)-modules.