Generators of the pro-p Iwahori and Galois representations

TL;DR

This paper identifies minimal generators for the pro-p Iwahori subgroup of split reductive groups over Z_p and constructs Galois extensions of Q with Galois groups related to these subgroups for large primes.

Contribution

It provides a minimal generating set for the pro-p Iwahori subgroup and constructs specific Galois extensions linked to these subgroups for large primes.

Findings

Minimal generators for the pro-p Iwahori subgroup identified

Galois extensions of Q constructed with groups between pro-p and Iwahori subgroups

Results applicable for large regular primes p

Abstract

For an odd prime p, we determine a minimal set of topological generators of the pro-p Iwahori subgroup of a split reductive group G over Z\_p. In the simple adjoint case and for any sufficiently large regular prime p, we also construct Galois extensions of Q with Galois group between the pro-p and the standard Iwahori subgroups of G.