IWASAWA THEORY AND THE REPRESENTATIONS OF FINITE GROUPS
Abstract
Abstract We 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, we study $\mathbb {Z}_\ell $ -towers of Cayley graphs and the asymptotic growth of their Jacobians. The main result establishes that the Iwasawa polynomial associated to such a tower admits a canonical factorisation indexed by the irreducible representations of the underlying group. This leads to the definition of representation-theoretic Iwasawa polynomials, whose properties are studied.
Fields of Study & Subjects
Finite Group Theory Research
Publication details
- Journal / source
- Bulletin of the Australian Mathematical Society
- Publisher
- Cambridge University Press (CUP)
- Pages
- 1–13
- Publication date
- 20 May 2026
- Language
- EN