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Title: Galois Correspondence and Fourier Analysis on Local Discrete Subfactors
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 Bischoff et al. (J Funct Anal 281(1):109004, 2021), 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 đ›Œ-induction and 𝜎-restriction for braided subfactors previously known in the finite index case.  more » « less
Award ID(s):
1821162
PAR ID:
10325943
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Annales Henri Poincaré
ISSN:
1424-0637
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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