Cauchy identities for Grothendieck polynomials and a dual RSK correspondence through pipe dreams

Hugh Dennin

The Cauchy identity gives a recipe for decomposing a double Grothendieck polynomial ${\mathfrak{G}}_w^{({\hat{I}}^2)}(x;y)$ as a sum of products $\mathfrak{G}^{(β)}_v(x)\mathfrak{G}^{(β)}_u…