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Journal Article

#### The first pro-p-Iwahori cohomology of mod-p principal series for
p-adic GL_{n}

##### External Resource

https://doi.org/10.1090/tran/7619

(Publisher version)

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##### Fulltext (public)

arXiv:1708.03014.pdf

(Preprint), 565KB

##### Supplementary Material (public)

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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.

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.