Connection between Schubert polynomials and top Lascoux polynomials

Schubert polynomials form a basis of the polynomial ring ℚx 1, x 2, ⋯. This basis and its structure constants have received extensive study. Recently, Pan and Yu initiated the study of top Lascoux polynomials. These polynomials form a basis of the vector space V ^, a sub-algebra of ℚx 1, x 2, ⋯ where each graded piece has finite dimension. This paper connects Schubert polynomials and top Lascoux polynomials via a simple operator. We use this connection to show these two bases share the same structure constants. We also translate several results on Schubert polynomials to top Lascoux polynomials, including combinatorial formulas for their monomial expansions and supports.