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

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:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>M</m:mi> <m:mi>n</m:mi> </m:msub> </m:math> Mₙ with maximal nilpotency class. For representation dimensions coprime to all primes <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>p</m:mi> <m:mo><</m:mo> <m:mi>n</m:mi> </m:mrow> </m:math> p<n , we construct all irreducible representations of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>M</m:mi> <m:mi>n</m:mi> </m:msub> </m:math> Mₙ by defining a standard form for the matrices of these representations.