Irreducible representations of a family of groups of maximal nilpotency class I: the non-exceptional case

Abstract

We use a constructive method to obtain all but finitely many p-local representation zeta functions of a family Mn of finitely generated nilpotent groups with maximal nilpotency class. For representation dimensions coprime to all primes p < n, we construct all irreducible representations of Mn by defining a standard form for the matrices of these representations and, after taking into account twisting and isomorphism, count these twist isoclasses to obtain our p-local zeta functions.