Presentation of the Iwasawa algebra of the pro-$p$ Iwahori subgroup of $G{L}_n({\mathbb{Z}}_p)$

Iwasawa algebras of compact $p$-adic Lie groups are completed group algebras with applications in number theory in studying class numbers of towers of number fields and representation theory of $p$-adic Lie groups. In our earlier work, we determined an explicit presentation of the Iwasawa algebra for the first principal congruence kernel of Chevalley groups over ${\mathbb{Z}}_p$. In this paper, for prime $p>n+1$, we extend our result to determine the explicit presentation, in the form of generators and relations, of the Iwasawa algebra of the pro-$p$ Iwahori subgroup of $G{L}_n({\mathbb{Z}}_p)$.