AI 中文总结
该研究针对剩余域为𝔽ₚ真扩域且p>3的非阿基米德局部域F，证明非环面连通约化群G存在特定模p表示，进而说明pro-p-Iwahori不变量函子无法诱导对应范畴间的等价关系，与GL₂(ℚₚ)的情形不同。
AI 中文摘要
设F为非阿基米德局部域，其剩余域是𝔽ₚ的真扩域且p>3。我们推广Ghate-Le-Sheth的结果，证明F上任意非环面的连通约化群G均存在光滑不可约非容许的模p表示。由此可得，pro-p-Iwahori不变量函子无法诱导由其pro-p-Iwahori不变量向量生成的光滑模p G表示范畴与pro-p-Iwahori-Hecke代数模之间的等价关系，这与GL₂(ℚₚ)的情形相反。
英文摘要
Suppose $F$ is a nonarchimedean local field whose residue field is a proper extension of $\mathbb{F}_p$ with $p > 3$. Generalizing results of Ghate--Le--Sheth, we show that any split, connected, reductive group $G$ over $F$ which is not a torus admits a smooth, irreducible, non-admissible mod $p$ representation. We use this to show that the functor of pro-$p$-Iwahori invariants does not induce an equivalence between the category of smooth mod $p$ $G$-representations generated by their pro-$p$-Iwahori invariant vectors and modules over the pro-$p$-Iwahori--Hecke algebra, contrary to what happens for $\textrm{GL}_2(\mathbb{Q}_p)$.
Comments8 pages. Comments welcome!
