Presentation of an Iwasawa algebra : the case of \Gamma_1 SL(2,Z_p)

Abstract : Assume G is a semi-simple Chevalley group, so G(Zp ) ⊂ G(Qp ) is a max- imal compact subgroup. Both the p-adic representation theory of G(Qp ) and non-commutative Iwasawa theory involve the Iwasawa algebra of G(Zp ) or suitable congruence subgroups. It seems to have been assumed that explicit descriptions, by generators and relations, of these algebras were inaccessi- ble. However, it is a general principle that natural ob jects coming from semi-simple (split) groups have explicit presentations. Famous examples are Serre's presentation of the semi-simple algebras and Steinberg's presentation of the Chevalley groups [7, 8]. In this paper we will give a presentation for the Iwasawa algebra of the subgroup of level 1 in S L(2, Z) (p
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Laurent Clozel. Presentation of an Iwasawa algebra : the case of \Gamma_1 SL(2,Z_p). 2011. 〈hal-00617986〉

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