| Autor: |
Aiello, Valeriano, Jones, Vaughan F. R. |
| Rok vydání: |
2019 |
| Předmět: |
|
| Zdroj: |
J. Funct. Anal. 2021 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.jfa.2020.108777 |
| Popis: |
The Hilbert space $\mathcal H$ of backward renormalisation of an anyonic quantum spin chain affords a unitary representation of Thompson's group $F$ via local scale transformations. Given a vector in the canonical dense subspace of $\mathcal H$ we show how to calculate the corresponding spectral measure for any element of $F$ and illustrate with some examples. Introducing the "essential part" of an element we show that the spectral measure of any vector in $\mathcal H$ is, apart from possibly finitely many eigenvalues, absolutely continuous with respect to Lebesgue measure. The same considerations and results hold for the Brown-Thompson groups $F_n$ (for which $F=F_2$). |
| Databáze: |
arXiv |
| Externí odkaz: |
|
