Littlewood–Richardson coefficients for Grothendieck polynomials from integrability

M Wheeler; P Zinn-Justin

Journal article

Littlewood–Richardson coefficients for Grothendieck polynomials from integrability

M Wheeler, P Zinn-Justin

Journal Fur Die Reine Und Angewandte Mathematik | WALTER DE GRUYTER GMBH | Published : 2019

DOI: 10.1515/crelle-2017-0033

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.

University of Melbourne Researchers

Michael Wheeler Author

Paul Zinn-Justin Author

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Grants

Awarded by Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers

Funding Acknowledgements

MW is supported by the ARC grant DE160100958 and the ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS). PZJ is supported by ERC grant "LIC" 278124, ARC grants DP140102201 and FT150100232.