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Stable Grothendieck polynomials and K-theoretic factor sequences

Anders S. Buch·Andrew Kresch·Mark Shimozono·Harry Tamvakis·Alexander Yong
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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 $K$-theoretic analogue of the factor sequence formula of [Buch-Fulton '99] for the cohomological quiver polynomials.

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Anders S. Buch, Andrew Kresch, Mark Shimozono, Harry Tamvakis, Alexander Yong. 2006-01-21. Stable Grothendieck polynomials and K-theoretic factor sequences. https://arxiv.org/abs/math/0601514

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