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Symmetric Grothendieck polynomials are analogues of Schur polynomials in theK-theory of Grassmannians. We build dual families of symmetric Grothendieckpolynomials using Schur operators. With this approach we prove skew Cauchyidentity and then derive various applications: skew Pieri rules, dualfiltrations of Young's lattice, generating series and enumerative identities.We also give a new explanation of the finite expansion property for products ofGrothendieck polynomials.

Symmetric Grothendieck polynomials, skew Cauchy identities, and dual filtered Young graphs