Refine search
Actions for selected content:
2 results
IWASAWA THEORY AND THE REPRESENTATIONS OF FINITE GROUPS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 20 May 2026, pp. 1-13
-
- Article
-
- You have access
- HTML
- Export citation
-
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.
Polyhedral groups in
$\textbf{G}_{\textbf{2}}(\mathbb C)$
- Part of
-
- Journal:
- Glasgow Mathematical Journal / Volume 65 / Issue S1 / May 2023
- Published online by Cambridge University Press:
- 11 August 2022, pp. S123-S128
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
We classify embeddings of the finite groups
$A_4$, 
$S_4$ and 
$A_5$ in the Lie group 
$G_2(\mathbb C)$ up to conjugation.
