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arXiv · 2512.19045

Classical double Grothendieck transitions

Eric Marberg
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Abstract

Kirillov and Naruse have constructed double Grothendieck polynomials to represent the equivariant K-theory classes of Schubert varieties in the complete flag manifolds of types B, C, and D. We derive a recursive formula for these polynomials, extending certain K-theoretic transition equations known in type A to all classical types. As an application, we obtain an identity that expands the K-Stanley symmetric functions in types B, C, and D into positive linear combinations of K-theoretic Schur P- and Q-functions. We also resolve several positivity conjectures related to the skew generalizations of the latter functions.

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Eric Marberg. 2025-12-22. Classical double Grothendieck transitions. https://arxiv.org/abs/2512.19045

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