Galois Correspondence and Fourier Analysis on Local Discrete Subfactors

Abstract

Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity condition motivated by the study of inclusion of Quantum Field Theories in the algebraic Haag-Kastler setting. In [BDG21], we proved that every irreducible local discrete subfactor arises as the fixed point subfactor under the action of a canonical compact hypergroup. In this work, we prove a Galois correspondence between intermediate von Neumann algebras and closed subhypergroups, and we study the subfactor theoretical Fourier transform in this context. Along the way, we extend the main results concerning $\alpha$-induction and $\sigma$-restriction for braided subfactors previously known in the finite index case.

arXiv comment33 pages

References in corpus (27)

• Nets of Subfactors
• Modular Invariants, Graphs and $\alpha$-Induction for Nets of Subfactors. III
• Applications of braided endomorphisms from conformal inclusions
• Planar algebras, I
• On $\alpha$-induction, chiral generators and modular invariants for subfactors
• Chiral structure of modular invariants for subfactors
• Modular Invariants, Graphs and $\alpha$-Induction for Nets of Subfactors I
• Modular Invariants, Graphs and $\alpha$-Induction for Nets of Subfactors II
• Tensor categories and endomorphisms of von Neumann algebras (with applications to Quantum Field Theory)
• Subfactor realisation of modular invariants
• Noncommutative Uncertainty Principles
• Quantum Fourier Analysis
• Generalized Orbifold Construction for Conformal Nets
• Minimal index and dimension for 2-$C^{\ast }$-categories with finite-dimensional centers
• On Landauer's principle and bound for infinite systems
• N=2 superconformal nets
• Phase boundaries in algebraic conformal QFT
• Classification of Subsystems for Local Nets with Trivial Superselection Structure
• Superselection Theory for Subsystems
• Compact Hypergroups from Discrete Subfactors
• Infinite index extensions of local nets and defects
• Realization of rigid C${}^{\ast }$-tensor categories via Tomita bimodules
• Classification of subsystems for graded-local nets with trivial superselection structure
• On the Jones index values for conformal subnets
• Braided categories of endomorphisms as invariants for local quantum field theories
• A Comment on Jones Inclusions with infinite Index
• Hardy-Littlewood inequality and $L^p$-$L^q$ Fourier multipliers on compact hypergroups

Cited by in corpus (6)

• Non-invertible symmetries act locally by quantum operations
• Haploid algebras in $C^{\ast }$-tensor categories and the Schellekens list
• Bayesian inversion and the Tomita-Takesaki modular group
• Quantum Operations on Conformal Nets
• von Neumann Subfactors and Non-invertible Symmetries
• A planar algebraic description of conditional expectations