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

2014/07/10 by Shannon Ezzat, Ezzat, Shannon
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1407.2902

16 pages

arxiv created 2014/07/10 · arxiv updated 2014/07/11

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.

Related

• Representation zeta function of a family of maximal class groups: various exceptional cases
• Representation growth of maximal class groups: various exceptional cases
• Representation zeta functions of groups of type A₂ in positive characteristic
• Counting Irreducible Representations of the Discrete Heisenberg Group Over the Integers of a quadratic number field
• Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces