Explicit presentation of an Iwasawa algebra: The case of pro-p Iwahori subgroup of SL _n (ℤ _p )

Abstract

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. We previously determined an explicit presentation of the Iwasawa algebra for the first principal congruence kernel of Chevalley groups over Zp. 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 GLn(Zp).