The first pro-p-Iwahori cohomology of mod-p principal series for p-adic GLn

Kozioł, Karol

doi:10.1090/tran/7619

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The first pro-p-Iwahori cohomology of mod-p principal series for p-adic GL_n

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Kozioł, Karol
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1090/tran/7619
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arXiv:1708.03014.pdf
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Citation

Kozioł, K. (2019). The first pro-p-Iwahori cohomology of mod-p principal series for p-adic GL_n. Transactions of the American Mathematical Society, 372(2), 1237-1288. doi:10.1090/tran/7619.

Cite as: https://hdl.handle.net/21.11116/0000-0004-68EB-F

Abstract

Let $p\geq 3$ be a prime number and $F$ a $p$-adic field. Let $I_1$ denote the pro-$p$-Iwahori subgroup of $\textrm{GL}_n(F)$, and $\mathcal{H}$ the
pro-$p$-Iwahori--Hecke algebra of $\textrm{GL}_n(F)$ with respect to $I_1$
(over a coefficient field of characteristic $p$). We compute the structure of
$\textrm{H}^1(I_1,\pi)$ as an $\mathcal{H}$-module, where $\pi$ is a mod-$p$ principal series representation of $\textrm{GL}_n(F)$. We also give some
partial results about the structure of $\textrm{H}^1(I_1,\pi)$ for a general
split reductive group with irreducible root system.