Representation zeta function of a family of maximal class groups: Non-exceptional primes

Abstract

We use a constructive method to obtain all but finitely many 𝑝-local representation zeta functions of a family of finitely generated nilpotent groups M n M_{n} with maximal nilpotency class. For representation dimensions coprime to all primes p < n p<n , we construct all irreducible representations of M n M_{n} by defining a standard form for the matrices of these representations.