Stable Grothendieck polynomials and K-theoretic factor sequences
Abstract
We formulate a nonrecursive combinatorial rule for the expansion of the stable Grothendieck polynomials of [Fomin-Kirillov '94] in the basis of stable Grothendieck polynomials for partitions. This gives a common generalization, as well as new proofs of the rule of [Fomin-Greene '98] for the expansion of the stable Schubert polynomials into Schur polynomials, and the K-theoretic Grassmannian Littlewood-Richardson rule of [Buch '02]. The proof is based on a generalization of the Robinson-Schensted and Edelman-Greene insertion algorithms. Our results are applied to prove a number of new formulas and properties for K-theoretic quiver polynomials, and the Grothendieck polynomials of [Lascoux-Schutzenberger '82]. In particular, we provide the first -theoretic analogue of the factor sequence formula of [Buch-Fulton '99] for the cohomological quiver polynomials.
Cite
@article{arxiv.math/0601514,
title = {Stable Grothendieck polynomials and K-theoretic factor sequences},
author = {Anders S. Buch and Andrew Kresch and Mark Shimozono and Harry Tamvakis and Alexander Yong},
journal= {arXiv preprint arXiv:math/0601514},
year = {2010}
}
Comments
21 pages