Galois Correspondence and Fourier Analysis on Local Discrete Subfactors

Discrete subfactors include a particular class of infinite index and all finite ones. A discrete subfactor is called local when it braided fulfills commutativity condition motivated by the study inclusion Quantum Field Theories in algebraic Haag–Kastler setting. In Bischoff et al. (J Funct Anal 281(1):109004, 2021), we proved that every irreducible arises as fixed point under action canonical compact hypergroup. this work, prove Galois correspondence between intermediate von Neumann algebras closed subhypergroups, theoretical Fourier transform context. Along way, extend main results concerning $$\alpha $$ -induction $$\sigma -restriction for previously known case.