论文标题
$ p $ -adic $ \ mathrm {gl} _ {n} $ in STRUTIS $ P $中的不可用的不可减至的表示
Non-admissible irreducible representations of $p$-adic $\mathrm{GL}_{n}$ in characteristic $p$
论文作者
论文摘要
令$ p> 3 $和$ f $是一个非Archimedean本地字段，其残留字段的适当有限扩展名为$ \ Mathbb {f} _p $。我们构建平滑的$ \ mathrm {gl} _2（f）$ $ f $的$ \ mathrm {gl} _2（f）$的平滑表征，以$ f $的较早结果为$ f $ to $ f $ to $ \ mathbb {q} _ {p} $。该结构使用了Breuil和Paskunas的图表理论。通过抛物线诱导，我们获得了$ \ mathrm {gl} _n（f）$ $ n> 2 $的$ \ mathrm {gl} _n（f）$的平滑表现。
Let $p>3$ and $F$ be a non-archimedean local field with residue field a proper finite extension of $\mathbb{F}_p$. We construct smooth absolutely irreducible non-admissible representations of $\mathrm{GL}_2(F)$ defined over the residue field of $F$ extending the earlier results of the authors for $F$ unramified over $\mathbb{Q}_{p}$. This construction uses the theory of diagrams of Breuil and Paskunas. By parabolic induction, we obtain smooth absolutely irreducible non-admissible representations of $\mathrm{GL}_n(F)$ for $n>2$.
