Presentation of an Iwasawa algebra:The pro-$p$-Iwahori of reductive groups

TL;DR

This paper provides an explicit algebraic presentation of the Iwasawa algebra associated with the pro-$p$ Iwahori subgroup of a split reductive group over $Q_p$, extending previous results for specific cases.

Contribution

It generalizes prior work to give a complete ring-theoretic presentation for the Iwasawa algebra of pro-$p$ Iwahori subgroups in a broad class of reductive groups.

Findings

Explicit generators and relations for the Iwasawa algebra are established.

The presentation extends known results from $SL_2$ and $SL_n$ to general reductive groups.

The work facilitates further algebraic and number-theoretic investigations.

Abstract

In this article we generalize results of Clozel and Ray (for $SL_2$ and $SL_n$ respectively) to give explicit ring-theoretic presentation in terms of a complete set of generators and relations of the Iwasawa algebra of the pro-$p$ Iwahori subgroup of a connected, split, reductive group $\mathbb{G}$ over $\mathbb{Q}_p$.