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arXiv · 2610.34607

A proof of the Grothendieck join-meet positivity

Peter L. Guo·Mingyang Kang·Jiaji Liu·Rui Xiong
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Abstract

We prove the (signed) Grothendieck join--meet positivity $$ G_{λ\veeμ}G_{λ\wedgeμ} -G_λG_μ\in \sum_ν \mathbb{N}\cdot (-1)^{|ν|-|λ|-|μ|}G_ν$$ for stable Grothendieck polynomials using geometric Satake equivalence, thereby resolving a conjecture posed by Thomas and Yong.

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Peter L. Guo, Mingyang Kang, Jiaji Liu, Rui Xiong. 2026-10-25. A proof of the Grothendieck join-meet positivity. https://arxiv.org/abs/2610.34607

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