Littlewood-Richardson coefficients for Grothendieck polynomials from integrability

2016/07/08 by Wheeler, Michael, Zinn-Justin, Paul · 2 citations
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1607.02396

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.

Cited by

• Inhomogeneous q-Whittaker Polynomials I: Duality and Expansions
• Quantum Difference Equations for Grassmannians

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