We introduce fusion bialgebras and their duals and systematically study their Fourier
analysis. As an application, we discover new efficient analytic obstructions on the unitary …

The main purpose of this paper is to classify exchange relation planar algebras with 4
dimensional 2-boxes. Besides its skein theory, we emphasize the positivity of subfactor …

Jones introduced some unitary representations of Thompson group F constructed from a
given subfactor planar algebra, and all unoriented links arise as matrix coefficients of these …

In this paper, we investigate quantum Fourier analysis on subfactors and unitary fusion
categories. We prove the complete positivity of the comultiplication for subfactors and derive …

In this paper, we introduce Frobenius von Neumann algebras and study quantum
convolution inequalities. In this framework, we unify quantum Young's inequality on quantum …

In this note, we discuss the notion of symmetric self-duality of shaded planar algebras, which
allows us to lift shadings on subfactor planar algebras to obtain Z/2Z-graded unitary fusion …

Not all planar algebras can encode the algebraic structure of a Yang–Baxter integrable
model described in terms of a so-called homogeneous transfer operator. In the family of …

Vaughan Jones made fundamental contributions to mathematics and mathematical physics,
bringing together disparate areas of operator algebras, knots, links and low-dimensional …

We compute the fusion rule of a one-parameter family of spherical categories constructed by
one author from the classification of singly generated Yang–Baxter planar algebras. The …

Bisch and Jones proposed the classification of planar algebras by simple generators and
relations. They investigated with the second author the classification of planar algebras …