##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Shishir Agrawal

#### UCSD

## From category $\mathcal{O}^\infty$ to locally analytic representations

##### Abstract:

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]

### October 13, 2022

### 2:00 PM

APM 6402 and Zoom

See https://www.math.ucsd.edu/~nts

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