A proof of the Grothendieck join-meet positivity

Source 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.