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arXiv · 1906.01286

On some properties of symplectic Grothendieck polynomials

Eric Marberg·Brendan Pawlowski
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Abstract

Grothendieck polynomials, introduced by Lascoux and Sch\"utzenberger, are certain $K$-theory representatives for Schubert varieties. Symplectic Grothendieck polynomials, described more recently by Wyser and Yong, represent the $K$-theory classes of orbit closures for the complex symplectic group acting on the complete flag variety. We prove a transition formula for symplectic Grothendieck polynomials and study their stable limits. We show that each of the $K$-theoretic Schur $P$-functions of Ikeda and Naruse arises from a limiting procedure applied to symplectic Grothendieck polynomials representing certain "Grassmannian" orbit closures.

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Eric Marberg, Brendan Pawlowski. 2019-06-04. On some properties of symplectic Grothendieck polynomials. https://doi.org/10.1016/j.jpaa.2020.106463

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