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- W4301973733 abstract "We establish a poset structure on combinatorial bases of multivariate polynomials defined by positive expansions, and study properties common to bases in this poset. Included are the well-studied bases of Schubert polynomials, Demazure characters and Demazure atoms; the quasi-key, fundamental and monomial slide bases introduced in 2017 by Assaf and the author; and a new basis we introduce completing this poset structure. We show the product of a Schur polynomial and an element of a basis in this poset expands positively in that basis; in particular, we give the first Littlewood-Richardson rule for the product of a Schur polynomial and a quasi-key polynomial. This rule simultaneously extends Haglund, Luoto, Mason and van Willigenburg's (2011) Littlewood-Richardson rule for quasi-Schur polynomials and refines their Littlewood-Richardson rule for Demazure characters. We also establish bijections connecting combinatorial models for these polynomials including semi-skyline fillings and quasi-key tableaux." @default.
- W4301973733 created "2022-10-06" @default.
- W4301973733 creator A5063906754 @default.
- W4301973733 date "2017-07-04" @default.
- W4301973733 modified "2023-09-26" @default.
- W4301973733 title "Polynomial bases: positivity and Schur multiplication" @default.
- W4301973733 doi "https://doi.org/10.48550/arxiv.1707.01172" @default.
- W4301973733 hasPublicationYear "2017" @default.
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