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

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