23 citations · 55 across the 11 of their papers we have counts for
11 papers
Triangular Prism Equations and Categorification
Zhengwei Liu, Sebastien Palcoux, Yunxiang Ren +1
We introduce the triangular prism equations (TPE) for fusion categories, obtained by evaluating triangular prisms in terms of tetrahedra. Using an oriented graphical calculus, we s…
Learning particle swarming models from data with Gaussian processes
Jinchao Feng, Charles Kulick, Yunxiang Ren +1
Interacting particle or agent systems that display a rich variety of swarming behaviours are ubiquitous in science and engineering. A fundamental and challenging goal is to underst…
Interpolated family of non group-like simple integral fusion rings of Lie type
Zhengwei Liu, Sebastien Palcoux, Yunxiang Ren
This paper is motivated by the quest of a non-group irreducible finite index depth 2 maximal subfactor. We compute the generic fusion rules of the Grothendieck ring of Rep(PSL(2,q)…
Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six
Zhengwei Liu, Sebastien Palcoux, Yunxiang Ren
This paper classifies the Grothendieck rings of complex fusion categories of multiplicity one up to rank six. Among 72 possible fusion rings, ones are filtered out by using ca…
Quantum Fourier Analysis
Arthur Jaffe, Chunlan Jiang, Zhengwei Liu +2
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides inte…
A generating problem for subfactors
Yunxiang Ren
Bisch and Jones proposed the classification of planar algebras by simple generators and relations. In this paper, we study the generating problem for a family of group-subgroup sub…
Universal skein theory for group actions
Yunxiang Ren
Given a group action on a finite set, we define the group-action model which consists of tensor network diagrams which are invariant under the group symmetry. In particular, group-…
On Jones Subgroup of R. Thompson's Group
Jordan Nikkel, Yunxiang Ren
Jones introduced unitary representations for the Thompson groups and from a given subfactor planar algebra. Some interesting subgroups arise as the stabilizer of certain ve…
An angle between intermediate subfactors and its rigidity
Keshab Chandra Bakshi, Sayan Das, Zhengwei Liu +1
We introduce a new notion of angle between intermediate subfactors and prove various interesting properties of the angle and relate it with the Jones' index. We prove a uniform 60…
From skein theory to presentations for Thompson group
Yunxiang Ren
Jones introduced unitary representations of Thompson group starting from a given subfactor planar algebra, and all unoriented links arise as matrix coefficients of these repres…
Classification of Thurston-relation subfactor planar algebras
Corey Jones, Zhengwei Liu, Yunxiang Ren
Bisch and Jones suggested the skein theoretic classification of planar algebras and investigated the ones generated by 2-boxes with the second author. In this paper, we consider 3-…