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- W3185550792 abstract "Let $G$ be a $p$-adic Lie group with reductive Lie algebra $mathfrak{g}$. In analogy to the translation functors introduced by Bernstein and Gelfand on categories of $U(mathfrak{g})$-modules we consider similarly defined functors on the category of coadmissible modules over the locally analytic distribution algebra $D(G)$ on which the center of $U(mathfrak{g})$ acts locally finite. These functors induce equivalences between certain subcategories of the latter category. Furthermore, these translation functors are naturally related to those on category $mathcal{O}$ via the functors from category $mathcal{O}$ to the category of coadmissible modules. We also investigate the effect of the translation functors on locally analytic representations $Pi(V)^{rm la}$ associated by the $p$-adic Langlands correspondence for ${rm GL}_2(mathbb{Q}_p)$ to 2-dimensional Galois representations $V$." @default.
- W3185550792 created "2021-08-02" @default.
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- W3185550792 date "2021-07-18" @default.
- W3185550792 modified "2023-09-27" @default.
- W3185550792 title "Translation functors for locally analytic representations" @default.
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