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arXiv · 2603.23243

Shuffle algebra realizations for modular Yangians

Hao Chang·Hongmei Hu·Yue Hu
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Abstract

We study the shuffle algebra realization of positive modular Yangians of classical type over an algebraically closed field of characteristic $p>3$. We show that, unlike in characteristic zero, the natural shuffle homomorphism has a nontrivial kernel. Its image is characterized by a $p$-wheel condition, while its kernel is precisely the ideal generated by the $p$-th powers of the Lyndon root vectors. This identifies the corresponding quotient with the small Yangian arising from a $\mathbb Z[\frac12]$-integral form. As part of the construction, we establish a PBW basis for the integral form and obtain the PBW theorem and $p$-center results for the Drinfeld presentation of modular Yangians.

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Hao Chang, Hongmei Hu, Yue Hu. 2026-03-24. Shuffle algebra realizations for modular Yangians. https://arxiv.org/abs/2603.23243

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