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arXiv · 1607.02396

Littlewood-Richardson coefficients for Grothendieck polynomials from integrability

Michael Wheeler·Paul Zinn-Justin
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Abstract

We study the Littlewood-Richardson coefficients of double Grothendieck polynomials indexed by Grassmannian permutations. Geometrically, these are the structure constants of the equivariant $K$-theory ring of Grassmannians. Representing the double Grothendieck polynomials as partition functions of an integrable vertex model, we use its Yang-Baxter equation to derive a series of product rules for the former polynomials and their duals. The Littlewood-Richardson coefficients that arise can all be expressed in terms of puzzles without gashes, which generalize previous puzzles obtained by Knutson-Tao and Vakil.

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Michael Wheeler, Paul Zinn-Justin. 2016-07-08. Littlewood-Richardson coefficients for Grothendieck polynomials from integrability. https://arxiv.org/abs/1607.02396

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