Positivity of quiver coefficients through Thom polynomials

Anders S. Buch, László M. Fehér, Richárd Rimányi

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11 Scopus citations

Abstract

We use the Thom Polynomial theory developed by Fehér and Rimányi to prove the component formula for quiver varieties conjectured by Knutson, Miller, and Shimozono. This formula expresses the cohomology class of a quiver variety as a sum of products of Schubert polynomials indexed by minimal lace diagrams, and implies that the quiver coefficients of Buch and Fulton are non-negative. We also apply our methods to give a new proof of the component formula from the Gröbner degeneration of quiver varieties, and to give generating moves for the KMS-factorizations that form the index set in K-theoretic versions of the component formula.

Original languageEnglish (US)
Pages (from-to)306-320
Number of pages15
JournalAdvances in Mathematics
Volume197
Issue number1
DOIs
StatePublished - Oct 20 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Degeneracy loci
  • Quiver coefficients
  • Thom polynomials

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