# On some properties of symplectic Grothendieck polynomials

## TL;DR

This paper studies symplectic Grothendieck polynomials, proving a transition formula, analyzing their stable limits, and connecting them to K-theoretic Schur P-functions, advancing understanding of their algebraic and geometric properties.

## Contribution

It introduces a transition formula for symplectic Grothendieck polynomials and links their limits to K-theoretic Schur P-functions, expanding the theoretical framework.

## Key findings

- Proved a transition formula for symplectic Grothendieck polynomials.
- Analyzed stable limits of these polynomials.
- Connected limits to K-theoretic Schur P-functions.

## 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.