崔沛仪 , 刁晗生 , 杜衡 , 胡悦科 , ‌李华杰 , 徐文强 , 徐斌 , 朱艺航

Tasho Kaletha

2026年10月26日 10:00 至 11:00

Shuangqing-C654

The construction of representations of p-adic groups via Kim-Yu types contains a structural dychotomy: Depth-zero types arise geometrically via Deligne-Lusztig theory, while positive-depth types arise algebraically via the Weil-Heisenberg representation. Some recent work has extended the geometric method to positive depth, but under the limiting assumption that all occurring groups are unramified. In this talk we will present a geometric construction of Kim-Yu types that covers the ramified case. The main input is Deligne-Lusztig theory in the setting of non-reductive groups of the form $J=H\rtimes G$, where $H$ is the Heisenberg group associated to a symplectic vector space $(V,\eta)$ and $G$ is a reductive group acting on $(V,\eta)$. We will show that the cohomology of the resulting Deligne-Lusztig varieties realizes the Kim-Yu procedure twisted by a certain explicit sign character. This is joint work with Charlotte Chan and Xinwen Zhu.