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Integral forms for Yangians of classical type
Abstract
Let g be a simple Lie algebra of classical type. We construct a ℤ[1/2]-integral form of the Yangian Y(g) generated by divided powers of the positive and negative Drinfeld generators, and establish its triangular decomposition and PBW basis. Under the loop filtration, its associated graded algebra is the current algebra part of Garland's integral form. As applications, over an algebraically closed field of characteristic p>3, we identify the small Yangian with the restricted Yangian and classify their finite dimensional simple modules in terms of restricted Drinfeld polynomials.
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BibTeX
@misc{chang2026integral,
title = {{Integral forms for Yangians of classical type}},
author = {Hao Chang and Hongmei Hu and Yue Hu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05988},
eprint = {2610.05988},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05988},
}
RIS
TY - UNPB
TI - Integral forms for Yangians of classical type
AU - Hao Chang
AU - Hongmei Hu
AU - Yue Hu
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.05988
UR - https://arxiv.org/abs/2610.05988
AB - Let g be a simple Lie algebra of classical type. We construct a ℤ[1/2]-integral form of the Yangian Y(g) generated by divided powers of the positive and negative Drinfeld generators, and establish its triangular decomposition and PBW basis. Under the loop filtration, its associated graded algebra is the current algebra part of Garland's integral form. As applications, over an algebraically closed field of characteristic p>3, we identify the small Yangian with the restricted Yangian and classify their finite dimensional simple modules in terms of restricted Drinfeld polynomials.
ER -