Using five-vertex model wavefunctions, the author reproves the Guo-Sun identity and proves a new identity and duality for rectangular factorial Grothendieck polynomials.
Factorial Flagged Grothendieck Polynomials
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abstract
We show that the factorial flagged Grothendieck polynomials defined by flagged set-valued tableaux of Knutson-Miller-Yong can be expressed by a Jacobi-Trudi type determinant formula, generalizing the work of Hudson-Matsumura. In particular, we obtain an alternative proof of the tableau and determinant formulas of vexillary double Grothendieck polynomials, that have been obtained by Knutson-Miller-Yong and Hudson-Matsumura respectively. Moreover, we show that each factorial flagged Grothendieck polynomial can be obtained from a product of linear polynomials by applying K-theoretic divided difference operators.
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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.