Iwasawa theory and the representations of finite groups

Anwesh Ray

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arXiv · 2504.09236

Iwasawa theory and the representations of finite groups

Anwesh Ray

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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 $\mathbb{Z}_\ell$-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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Anwesh Ray. 2025-04-12. Iwasawa theory and the representations of finite groups. https://arxiv.org/abs/2504.09236

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