Littlewood–Richardson coefficients for Grothendieck polynomials from integrability
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- Michael Wheeler
- School of Mathematics and Statistics , University of Melbourne , Parkville , Victoria 3010 , Australia
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- Paul Zinn-Justin
- Laboratoire de Physique Théorique et Hautes Énergies , CNRS UMR 7589 and Université Pierre et Marie Curie (Paris 6) , 4 place Jussieu, 75252 Paris cedex 05 , France ; and School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia
説明
<jats:title>Abstract</jats:title> <jats:p>We study the Littlewood–Richardson coefficients of double Grothendieck polynomials indexed by Grassmannian permutations. Geometrically, these are the structure constants of the equivariant <jats:italic>K</jats:italic>-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.</jats:p>
収録刊行物
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- Journal für die reine und angewandte Mathematik (Crelles Journal)
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Journal für die reine und angewandte Mathematik (Crelles Journal) 2019 (757), 159-195, 2017-09-21
Walter de Gruyter GmbH
