Representation growth of maximal class groups: various exceptional cases

2014/10/18 by Shannon Ezzat, Ezzat, Shannon
Mathematics · #Finite Group Theory Research #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1410.4992

Abstract

This paper is a sequel to "Representation growth of maximal class groups: non-exceptional primes". We use a constructive method to calculate some exceptional cases of p-local representation zeta functions of a family of finitely generated nilpotent groups M_n with maximal nilpotency class. Using the machinery of the constructive method from the prequel paper we construct all irreducible representations of degree p^N for all N∈ ℕ for the group M_p+1 for a fixed prime p. We also construct all irreducible representations of degree 2^N for the group M₄. Together with the main result from the prequel, this gives us a complete understanding of the irreducible representations of the groups M₃ and M₄, along with their global representation zeta functions.

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