论文标题
从类别$ \ MATHCAL {O}^\ infty $到本地分析表示
From category $\mathcal{O}^\infty$ to locally analytic representations
论文作者
论文摘要
令$ g $为$ p $ - addic还原组，$ \ mathfrak {g} $它的lie代数。我们从与$ \ Mathfrak {g} $相关的bernstein-Gelfand-gelfand类别的扩展中构建一个函子$ \ Mathcal {O} $，以构建$ G $的本地分析表示类别，从而扩展了Orlik-Trauch的早期构建。 $ p $ addic对数在托里（Tori）上发挥了关键作用。在施耐德和teitelbaum的意义上，该函子与可允许表示的子类别中的图像相准确。在途中，我们在分布代数和相关亚代词的模块理论中建立了一些基本结果，例如张量 - 辅助辅助公式。我们还将我们的构造与Breuil和Schraen在$ P $ -ADIC LANGLANDS计划的背景下建立的某些表示形式联系起来。
Let $G$ be a $p$-adic reductive group and $\mathfrak{g}$ its Lie algebra. We construct a functor from the extension closure of the Bernstein-Gelfand-Gelfand category $\mathcal{O}$ associated to $\mathfrak{g}$ into the category of locally analytic representations of $G$, thereby expanding on an earlier construction of Orlik-Strauch. A key role in this new construction is played by $p$-adic logarithms on tori. This functor is shown to be exact with image in the subcategory of admissible representations in the sense of Schneider and Teitelbaum. En route, we establish some basic results in the theory of modules over distribution algebras and related subalgebras, such as a tensor-hom adjunction formula. We also relate our constructions to certain representations constructed by Breuil and Schraen in the context of the $p$-adic Langlands program.
