1999/09/16 by Anders S. Buch, Anders Skovsted Buch, Buch, Anders S.
Mathematics · #05E05 (Primary) 14M15 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #math.CO #msc:05E05 #msc:14M15
paper · pdf · doi:10.48550/arxiv.math/9909090
13 pages, 11 figures
arxiv created 1999/09/16 · openalex publication_date 1999/09/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In our joint paper with W. Fulton (math.AG/9804041) we prove a formula for the cohomology class of a quiver variety. This formula is general enough to give new expressions for all known types of Schubert polynomials. In the present paper we discuss the relationship between this formula and Stanley symmetric functions. We show that the coefficients obtained when a Stanley symmetric function is expressed in the basis of Schur functions are special cases of a class of generalized Littlewood-Richardson coefficients appearing in the formula for quiver varieties. We also prove that Fulton's universal Schubert polynomials (math.AG/9702012) satisfy the usual rule for a Schubert polynomial of a product of two permutations.