Presentation of the Iwasawa algebra of the first congruence kernel of a semi-simple, simply connected Chevalley group over ${\mathbb{Z}}_p$

Abstract

It is a general principle that objects coming from semi-simple, simply connected (split) groups have explicit presentations like Serre's presentation of semi-simple algebras and Steinberg's presentation of Chevalley groups. In this paper we give an explicit presentation (by generators and relations) of the Iwasawa algebra for the first congruence kernel of a semi-simple, simply connected Chevalley group over ${\mathbb{Z}}_p$, extending the proof given by Clozel for the group ${\Gamma }_1(S{L}_2({\mathbb{Z}}_p))$, the first congruence kernel of $S{L}_2({\mathbb{Z}}_p)$ for primes $p>2$.

18 pages