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.
Funding source: Australian Research Council
Award Identifier / Grant number: DE160100958
Award Identifier / Grant number: DP140102201
Award Identifier / Grant number: FT150100232
Funding source: H2020 European Research Council
Award Identifier / Grant number: LIC 278124
Funding statement: 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.
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