Iwasawa theory and the representations of finite groups

2025/04/12 by Ray, Anwesh
#05C25 #11R23 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.09236

Abstract

In this note, I develop a representation-theoretic refinement of the Iwasawa theory of finite Cayley graphs. Building on analogies between graph zeta functions and number-theoretic L-functions, I study ℤ_ℓ-towers of Cayley graphs and the asymptotic growth of their Jacobians. My main result establishes that the Iwasawa polynomial associated to such a tower admits a canonical factorization indexed by the irreducible representations of the underlying group. This leads to the definition of representation-theoretic Iwasawa polynomials, whose properties are studied.

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