PreprintCC BY 4.0arXiv
Integral Forms of Twisted Quantum Affine Algebras and Quantum Frobenius
Abstract
For twisted quantum affine algebras, we compare Lusztig's restricted integral form with the integral form generated by group-like toral elements and divided powers of real Drinfeld current modes. The two forms coincide over ℤ[q,q−1] outside type A2n(2). In type A2n(2), the smallest ordinary localization over which they coincide is ℤ[q,q−1][Φ4r(q)−1| r≥1] when n=1, and ℤ[q,q−1][Φ8r(q)−1| r≥1] when n≥2, where Φk(q) are cyclotomic polynomials. In particular, no localization obtained by inverting finitely many nonzero Laurent polynomials suffices in this family.
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BibTeX
@misc{jiang2026integral,
title = {{Integral Forms of Twisted Quantum Affine Algebras and Quantum Frobenius}},
author = {Ziyang Jiang and Naihuan Jing},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36605},
eprint = {2610.36605},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36605},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Integral Forms of Twisted Quantum Affine Algebras and Quantum Frobenius
AU - Ziyang Jiang
AU - Naihuan Jing
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36605
UR - https://arxiv.org/abs/2610.36605
AB - For twisted quantum affine algebras, we compare Lusztig's restricted integral form with the integral form generated by group-like toral elements and divided powers of real Drinfeld current modes. The two forms coincide over ℤ[q,q^−1] outside type A_2n^(2). In type A_2n^(2), the smallest ordinary localization over which they coincide is ℤ[q,q^−1][Φ_4r(q)^−1| r≥1] when n=1, and ℤ[q,q^−1][Φ_8r(q)^−1| r≥1] when n≥2, where Φ_k(q) are cyclotomic polynomials. In particular, no localization obtained by inverting finitely many nonzero Laurent polynomials suffices in this family.
ER -