We study solvable lattice models associated to canonical Grothendieck polynomials and their duals. We derive inversion relations and Cauchy identities. Contents 1. Introduction 1 2. Row Vertex Models 3 2.1. Definition of Physical space. 3 2.2. Row vertex model for canonical Grothendieck polynomials. 3 2.3. Row vertex model for dual canonical Grothendieck polynomials. 9 3. Column Vertex Models 3.1. Definition of Physical space. 3.2. Column vertex model for canonical Grothendieck polynomials. 3.3. Column vertex model dual canonical Grothendieck polynomials. 3.4. Vertex model for j polynomials. 4. Generalised polynomials 4.1. Difference property of the R matrices. 4.2. Generalised polynomials. 5. Duality between Column and Row models 6. Cauchy identities Appendix A. RLL relations A.1. RLL for column model of G (α,β) λ . A.2. RLL relation for row model of g (α,β) λ . A.3. RLL for column model of g (α,β) λ . A.4. RLL for the Cauchy Identity. References

We study exactly solvable lattice models associated to canonical Grothendieck polynomials and their duals. We derive inversion relations and Cauchy identities.

We introduce the edge Schur functions E λ that are defined as a generating series over edge labeled tableaux. We formulate E λ as the partition function for a solvable lattice model, which we use to show they are symmetric polynomials and derive a Cauchy-type identity with factorial Schur polynomials. Finally, we give a crystal structure on edge labeled tableau to give a positive Schur polynomial expansion of E λ and show it intertwines with an uncrowding algorithm.