Logarithmic Concavity and sl2(C)

We observe that for any logarithmically concave finite sequence a0, a1, …, an of positive integers there is a representation of the Lie algebra sl2(C) from which this logarithmic concavity follows. Thus, in applying this strategy to prove logarithmic concavity, the only issue is to construct such a representation naturally from given combinatorial data. As an example, we do this when aj is the number of j-element stable sets in a claw-free graph, reproving a theorem of Hamidoune.