Grothendieck polynomials and quiver formulas

Anders S. Buch, Andrew Kresch, Harry Tamvakis, Alexander Yong

Research output: Contribution to journalArticlepeer-review

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 Schützenberger.

Original languageEnglish (US)
Pages (from-to)551-567
Number of pages17
JournalAmerican Journal of Mathematics
Volume127
Issue number3
DOIs
StatePublished - Jun 2005
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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