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arXiv · 1711.09544

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

Damir Yeliussizov
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Abstract

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

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Damir Yeliussizov. 2018-09-14. Symmetric Grothendieck polynomials, skew Cauchy identities, and dual filtered Young graphs. https://arxiv.org/abs/1711.09544

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