Combinatorics and Representation Theory of Special Cases of Chern Plethysm

TL;DR

This paper provides combinatorial interpretations for specific cases of Chern plethysm, a geometric method for generating Schur positive symmetric polynomials, and connects these to symmetric group modules.

Contribution

It introduces combinatorial interpretations for certain Chern plethysm cases and constructs symmetric group modules generalizing previous results.

Findings

Combinatorial interpretations for special Chern plethysm cases

Construction of symmetric group modules with Frobenius characteristics

Generalization of Reiner and Webb's results

Abstract

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.