Positivity of quiver coefficients through Thom polynomials

2003/11/12 by A. S. Buch, Anders Skovsted Buch, L Fehér +6
Mathematics · Physics and Astronomy · #05E15 #14N10 #57R45 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:05E15 #msc:14N10 #msc:57R45

paper · pdf · doi:10.48550/arxiv.math/0311203

12 pages

arxiv created 2003/11/12 · openalex publication_date 2003/11/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let r be an orbit of the quiver representation of type A_n (equioriented case). In this paper we study the Poincare dual of the closure of r (a.c.a. Thom polynomial/degeneracy loci formula) in equivariant cohomology. Using general Thom polynomial theory we prove the component formula and its stable version of [Knutson-Miller-Shimozono] as well as the positivity of the quiver coefficients of [Buch-Fulton]. We also show how the component formula follows from Grobner degeneration easily. In relation with the K-theory counterpart of the formula we give a new description of KMS factorizations based on transformations of lace diagrams.

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