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تسجيل مستخدم جديدGalois Correspondence and Fourier Analysis on Local Discrete Subfactors
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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.
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Growing out of the initial connections between subfactors and knot theory that gave rise to the Jones polynomial, Jones axiomatization of the standard invariant of an extremal finite index $II_1$ subfactor as a spherical $C^*$-planar algebra, present
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