let $g$ be a $p$-adic reductive group with $\mathfrak{g} = \mathrm{lie}(g)$. i will summarize work with matthias strauch in which we construct an exact functor from category $\mathcal{o}^\infty$, the extension closure of the bernstein-gelfand-gelfand category $\mathcal{o}$ inside the category of $u(\mathfrak{g})$-modules, into the category of admissible locally analytic representations of $g$. this expands on an earlier construction by sascha orlik and matthias strauch. a key role in our new construction is played by $p$-adic logarithms on tori, and representations in the image of this functor are related to some that are known to arise in the context of the $p$-adic langlands program.

[pre-talk at 1:20pm]