中俄数学研究生讨论班—Restriction to a hyperspecial subgroup: containing Steinberg
报告人：汪润泽（北京大学）
时间：2026-04-17 15:30-16:30
地点：智华楼四元厅
Abstract: Let $G$ be an unramified $p$-adic reductive group, $K$ a hyperspecial maximal compact subgroup, and $K/K^+\cong G(\mathbb F_q)$. Restricting an irreducible representation $V$ of $G(F)$ to $K$ gives a $G(\mathbb F_q)$-representation $V^{K^+}$. Prasad asked which $V$ have $V^{K^+}$ containing the Steinberg representation (or more generally any $π_λ$ attached to a Weyl group representation λ). This talk answers the first question completely. We also show that the irreducible components of $K^+$-fixed subspace lies in the Harish-Chandra principal series. The method also extends to the general case, providing a computable framework for the further study.
