Characteristic-free approaches around Yu's construction

TL;DR

This paper introduces a characteristic-free method for constructing twisted Heisenberg-Weil representations, extending Yu's construction to residual characteristic 2 and providing geometric realizations via Deligne-Lusztig theory.

Contribution

It presents a new characteristic-free approach to twisted Heisenberg-Weil representations and extends Yu's construction to characteristic 2, with geometric realizations and applications.

Findings

Constructed twisted Heisenberg-Weil representations without symmetric and ramified roots.

Extended Yu's construction to residual characteristic 2.

Provided explicit descriptions of positive-depth parahoric Deligne-Lusztig induction.

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.