In "Unimodality and Lie superalgebras" (citation below), Stanley uses the theory of Lie superalgebras to deduce some interesting combinatorial consequences about the unimodality of certain combinatorially defined sequences of numbers, and the Sperner property for certain finite posets.

Stanley, Richard P., Unimodality and Lie superalgebras, Stud. Appl. Math. 72, 263-281 (1985). ZBL0614.17004.