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A proof of the Grothendieck join-meet positivity
Abstract
We prove the (signed) Grothendieck join--meet positivity Gλ∨μGλ∧μ −GλGμ∈ ∑ν ℕ· (−1)|ν|−|λ|−|μ|Gν for stable Grothendieck polynomials using geometric Satake equivalence, thereby resolving a conjecture posed by Thomas and Yong.
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BibTeX
@misc{guo2026proof,
title = {{A proof of the Grothendieck join-meet positivity}},
author = {Peter L. Guo and Mingyang Kang and Jiaji Liu and Rui Xiong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34607},
eprint = {2610.34607},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34607},
}
RIS
TY - UNPB
TI - A proof of the Grothendieck join-meet positivity
AU - Peter L. Guo
AU - Mingyang Kang
AU - Jiaji Liu
AU - Rui Xiong
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34607
UR - https://arxiv.org/abs/2610.34607
AB - We prove the (signed) Grothendieck join--meet positivity G_λ∨μG_λ∧μ −G_λG_μ∈ ∑_ν ℕ· (−1)^|ν|−|λ|−|μ|G_ν for stable Grothendieck polynomials using geometric Satake equivalence, thereby resolving a conjecture posed by Thomas and Yong.
ER -