Stability of Products of Double Grothendieck Polynomials

Abstract We prove that products of double Grothendieck polynomials have the same back- and forward-stability numbers as products of Schubert polynomials, characterize which simple reflections appear in such products, and also give a new proof of a finiteness conjecture of Lam–Lee–Shimozono on products of back-stable Grothendieck polynomials, which was first proved by Anderson. To do this, we use the main theorems from our recent work, as well as expansion formulas of Lenart, Fomin–Kirillov, and Lam–Lee–Shimozono.