论文标题
统一表示的线性时期
Linear periods for unitary representations
论文作者
论文摘要
令$ f $为具有有限残基字段的特征零的本地非Archimedean字段。基于tadić的分类$ \ mathrm {gl} _ {2n}（f）$，我们将$ \ mathrm {gl} _ {gl} _ {2n}（f）$的不可约合的单一表示分类为非零固定时期，以speh代表为单位。我们还为SPEH表示的非零线性周期存在提供了必要的条件。
Let $F$ be a local non-Archimedean field of characteristic zero with a finite residue field. Based on Tadić's classification of the unitary dual of $\mathrm{GL}_{2n}(F)$, we classify irreducible unitary representations of $\mathrm{GL}_{2n}(F)$ that have nonzero linear periods, in terms of Speh representations that have nonzero periods. We also give a necessary and sufficient condition for the existence of a nonzero linear period for a Speh representation.
