Unimodal polynomials associated with Lie algebras and superalgebras (Q1184778)

Using the principal \(sl(2)\) embedding for simple Lie algebras, and the corresponding principally specialised characters of modules, the unimodality of certain polynomials can be proven. In the present paper, this idea is extended to principal \(osp(1,2)\) embeddings for simple Lie superalgebras. Some interesting unimodal polynomials associated with certain typical modules are treated, and a combinatorial interpretation is given. Using a new character formula for atypical modules of the Lie superalgebra \(sl(m/n)\), the principally specialised character is determined for this case too.