On spectral measures for certain unitary representations of R. Thompson's group F

Aiello, Valeriano; Jones, Vaughan F. R. (2021). On spectral measures for certain unitary representations of R. Thompson's group F. Journal of functional analysis, 280(1), p. 108777. Elsevier 10.1016/j.jfa.2020.108777

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The Hilbert space H of backward renormalisation of an anyonic quantum spin chain affords a unitary representation of Thompson’s group F via local scale transformations. The group F is discrete and mysterious in many ways so the obvious questions of irreducibility and distinctness of these representations appear difficult and in a first step towards solving them we calculate the spectral measures of group elements in the representation. Given a vector in the canonical dense subspace of H we calculate the corresponding spectral measure and illustrate with some examples. To do this calculation we introduce the “essential part” (intimately related to the conjugacy class) of an element. The spectral measure for any vector in 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 Fn (for which F = F2).

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Aiello, Valeriano

Subjects:

500 Science > 510 Mathematics

ISSN:

0022-1236

Publisher:

Elsevier

Funders:

[42] Schweizerischer Nationalfonds

Projects:

Projects 0 not found.

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

10 Feb 2022 09:55

Last Modified:

05 Dec 2022 16:05

Publisher DOI:

10.1016/j.jfa.2020.108777

BORIS DOI:

10.48350/164779

URI:

https://boris.unibe.ch/id/eprint/164779

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