Combinatorics and Representation Theory of Special Cases of Chern Plethysm

Chern plethysm, introduced by Billey, Rhoades, and Tewari, is a geometric way to produce Schur positive symmetric polynomials. We present combinatorial interpretations for the Schur expansions of special cases of Chern plethysm. We also exhibit a symmetric group module whose Frobenius characteristic is a symmetric function analog of one of these cases, generalizing a result of Reiner and Webb.