Double Grothendieck polynomials and colored lattice models
arXiv:2007.04533 · doi:10.1093/imrn/rnaa327
Abstract
We construct an integrable colored six-vertex model whose partition function is a double Grothendieck polynomial. This gives an integrable systems interpretation of bumpless pipe dreams and recent results of Weigandt [arXiv:2003.07342] relating double Grothendieck polynomias with bumpless pipe dreams. For vexillary permutations, we then construct a new model that we call the semidual version model. We use our semidual model and the five-vertex model of Motegi and Sakai to given a new proof that double Grothendieck polynomials for vexillary permutations are equal to flagged factorial Grothendieck polynomials. Taking the stable limit of double Grothendieck polynomials, we obtain a new proof that the stable limit is a factorial Grothendieck polynomial as defined by McNamara. The states of our semidual model naturally correspond to families of nonintersecting lattice paths, where we can then use the Lindström-Gessel-Viennot lemma to give a determinant formula for double Schubert polynomials corresponding to vexillary permutations.
arXiv comment24 pages, 10 figures; v2 minor corrections from referee reports
References in corpus (11)
- Stochastic higher spin vertex models on the line
- K-theoretic analogues of factorial Schur P- and Q-functions
- Vertex models, TASEP and Grothendieck polynomials
- Quantum Integrability and Generalised Quantum Schubert Calculus
- K-theoretic boson-fermion correspondence and melting crystals
- Multispecies TASEP and the tetrahedron equation
- Multispecies TASEP and combinatorial
- A Thom-Porteous formula for connective K-theory using algebraic cobordism
- Colored five-vertex models and Lascoux polynomials and atoms
- Inhomogeneous generalization of multispecies totally asymmetric zero range process
- Integrability approach to Feher-Nemethi-Rimanyi-Guo-Sun type identities for factorial Grothendieck polynomials