pith. machine review for the scientific record. sign in

arxiv: math/0306389 · v1 · submitted 2003-06-27 · 🧮 math.CO · math.AG

Recognition: unknown

Grothendieck polynomials and quiver formulas

Anders Skovsted Buch , Andrew Kresch , Harry Tamvakis , Alexander Yong
Authors on Pith no claims yet
classification 🧮 math.CO math.AG
keywords polynomialsgrothendieckformulaformulaslociquiverschubertalternating
0
0 comments X
read the original abstract

Fulton's universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear combinations of products of stable Grothendieck polynomials. We prove an explicit combinatorial formula for the coefficients, which shows that they have alternating signs. Our result is applied to obtain new expansions for the Grothendieck polynomials of Lascoux and Sch\"utzenberger.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials

    hep-th 2025-12 unverdicted novelty 7.0

    Schubert line defects in 3d GLSMs for complete flag manifolds are realized as SQM quivers whose indices give quantum Grothendieck polynomials and restrict the target space to Schubert varieties.