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Characteristic-free approaches around Yu's construction
Abstract
We give a direct characteristic-free construction of twisted Heisenberg-Weil representations when there are no symmetric and ramified roots. As a consequence, we show that twisted Yu's construction naturally extends to residual characteristic $2$. Moreover, we give a geometric realization of such twisted Heisenberg-Weil representations via the Deligne-Lusztig construction for Heisenberg group schemes. As an application, we give an explicit description of positive-depth parahoric Deligne-Lusztig induction in the generic case.
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BibTeX
@misc{takaya2026characteristicfree,
title = {{Characteristic-free approaches around Yu's construction}},
author = {Yuta Takaya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.03638},
eprint = {2605.03638},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.03638},
}
RIS
TY - UNPB
TI - Characteristic-free approaches around Yu's construction
AU - Yuta Takaya
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2605.03638
UR - https://arxiv.org/abs/2605.03638
AB - We give a direct characteristic-free construction of twisted Heisenberg-Weil representations when there are no symmetric and ramified roots. As a consequence, we show that twisted Yu's construction naturally extends to residual characteristic $2$. Moreover, we give a geometric realization of such twisted Heisenberg-Weil representations via the Deligne-Lusztig construction for Heisenberg group schemes. As an application, we give an explicit description of positive-depth parahoric Deligne-Lusztig induction in the generic case.
ER -