Irreducible Koopman representations for nonsingular actions on boundaries of rooted trees
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917946632175616 |
|---|---|
| author | Danilenko, Alexandre I. Dudko, Artem |
| author_facet | Danilenko, Alexandre I. Dudko, Artem |
| contents | Let $G$ be a countable branch group of automorphisms of a spherically homogeneous rooted tree. Under some assumption on finitarity of $G$, we construct, for each sequence $ω\in\{0,1\}^\Bbb N$, an irreducible unitary representation $κ_ω$ of $G$. Every two representations $κ_ω$ and $κ_{ω'}$ are weakly equivalent. They are unitarily equivalent if and only if $ω$ and $ω'$ are tail equivalent. Each $κ_ω$ appears as the Koopman representation associated with some ergodic $G$-quasiinvariant measure (of infinite product type) on the boundary of the tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03894 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irreducible Koopman representations for nonsingular actions on boundaries of rooted trees Danilenko, Alexandre I. Dudko, Artem Dynamical Systems Representation Theory 37A40, 22D10 Let $G$ be a countable branch group of automorphisms of a spherically homogeneous rooted tree. Under some assumption on finitarity of $G$, we construct, for each sequence $ω\in\{0,1\}^\Bbb N$, an irreducible unitary representation $κ_ω$ of $G$. Every two representations $κ_ω$ and $κ_{ω'}$ are weakly equivalent. They are unitarily equivalent if and only if $ω$ and $ω'$ are tail equivalent. Each $κ_ω$ appears as the Koopman representation associated with some ergodic $G$-quasiinvariant measure (of infinite product type) on the boundary of the tree. |
| title | Irreducible Koopman representations for nonsingular actions on boundaries of rooted trees |
| topic | Dynamical Systems Representation Theory 37A40, 22D10 |
| url | https://arxiv.org/abs/2503.03894 |