论文标题
Gelfand-Kirillov维度和$ P $ -ADIC JACQUET-LANGLANGS通信
Gelfand-Kirillov dimension and the $p$-adic Jacquet-Langlands correspondence
论文作者
论文摘要
我们绑定了$ p $ - 亚种还原基团的统一Banach空间表示的Gelfand-Kirillov维度，其本地分析矢量具有无限特征。我们使用BOND来研究Hecke Eigenspaces，以完整的Shimura曲线共同体和$ p $ -ADIC BANACH的空间表示形式超过$ \ MATHBB Q_P $出现在$ \ Mathbb Q_p $上，出现在$ p $ - p $ -Adic Jacquet-langlands对应的相应效果案例中，以造成良好的有效效果。
We bound the Gelfand-Kirillov dimension of unitary Banach space representations of $p$-adic reductive groups, whose locally analytic vectors afford an infinitesimal character. We use the bound to study Hecke eigenspaces in completed cohomology of Shimura curves and $p$-adic Banach space representations of the group of units of a quarternion algebra over $\mathbb Q_p$ appearing in the $p$-adic Jacquet-Langlands correspondence, deducing finiteness results in favourable cases.
