Unimodality and Lie Superalgebras

Abstract

It is well‐known how the representation theory of the Lie algebra sl(2, ℂ) can be used to prove that certain sequences of integers are unimodal and that certain posets have the Sperner property. Here an analogous theory is developed for the Lie superalgebra osp(1,2). We obtain new classes of unimodal sequences (described in terms of cycle index polynomials) and a new class of posets (the “super analogue” of the lattice L(m,n) of Young diagrams contained in an m × n rectangle) which have the Sperner property.