论文标题
甚至统一组的可降低性问题：深度为零案例
A reducibility problem for even unitary groups: The depth zero case
论文作者
论文摘要
我们研究了某些P-ADIC单一组中有关抛物线诱导的问题。更准确地说，对于$ e/f $，p-adic字段的二次扩展相关的统一组$ g = \ mathrm {u}（n，n，n，n，n，n，n）$包含一个抛物线子组$ p $，带有levi component $ l $ iSomorphic to $ \ shormorphic to $ \ mathrm {gl} _n（gl} _n（e）$。令$π$为零$ l $零的不可约的超质表示。我们使用Hecke代数方法来确定何时抛物面诱导的表示$ 〜r_p^gπ$可还原。
We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for $E/F$ a quadratic extension of p-adic fields the associated unitary group $G=\mathrm{U}(n,n)$ contains a parabolic subgroup $P$ with Levi component $L$ isomorphic to $\mathrm{GL}_n(E)$. Let $π$ be an irreducible supercuspidal representation of $L$ of depth zero. We use Hecke algebra methods to determine when the parabolically induced representation $ι_P^G π$ is reducible.
