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2023•arXiv (Cornell University)Open access

Combinatorics and Representation Theory of Special Cases of Chern Plethysm

Nathaniel Libman, Gidon Orelowitz

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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.

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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.

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Available 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.

Key concepts: Symmetric function, Stanley symmetric function, Symmetric group, Mathematics, Schur polynomial, Complete homogeneous symmetric polynomial, Ring of symmetric functions, Representation theory of the symmetric group

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