Using five-vertex model wavefunctions, the author reproves the Guo-Sun identity and proves a new identity and duality for rectangular factorial Grothendieck polynomials.
Grothendieck polynomials and the Boson-Fermion correspondence
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abstract
In this paper we study algebraic and combinatorial properties of Grothendieck polynomials and their dual polynomials by means of the Boson-Fermion correspondence. We show that these symmetric functions can be expressed as a vacuum expectation value of some operator that is written in terms of free-fermions. By using the free-fermionic expressions, we obtain alternative proofs of determinantal formulas and Pieri type formulas.
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Integrability approach to Feher-Nemethi-Rimanyi-Guo-Sun type identities for factorial Grothendieck polynomials
Using five-vertex model wavefunctions, the author reproves the Guo-Sun identity and proves a new identity and duality for rectangular factorial Grothendieck polynomials.