arXiv subjects
Publications and source records attributed to Marta Asaeda.
A series of pairs of graphs (Gamma_k, Gamma'_k), k = 0,1,2,... has been considered as candidates for dual pairs of principal graphs of subfactors of small Jones index above 4 and it has recently been proved that the pair (Gamma_k, Gamma'_k) comes from a subfactor if and only if k = 0 or k =1. We show that nevertheless there exists a unique fusion system compatible with this pair of graphs for all non-negative integers k.
We construct a noncommuting quadrilateral of factors whose upper sides are each the Asaeda-Haagerup subfactor with index $\frac{5+\sqrt{17}}{2} $ by showing the existence of a Q-system in the Asaeda-Haagerup category with index $\frac{7+\sqrt{17}}{2} $.
This article consists of six lectures on the categorification of the Burau representation and on link homology groups which categorify the Jones and the HOMFLY-PT polynomial. The notes are based on the lecture course at the PCMI 2006 summer school in Park City, Utah.
We show that any graph, in the sequence given by Haagerup in 1991 as that of candidates of principal graphs of subfactors, is not realized as a principal graph except for the smallest two. This settles the remaining case of a previous work of the first author.
The Galois group of the minimal polymonal of a Jones index value gives a new type of obstruction to a principal graph, thanks to a recent result of P.Etingof, D.Nikshych, and V.Ostrik. We show that the sequence of the graphs given by Haagerup as candidates of principal graphs of subfactors, are not realized as principal graphs for 7 7, and give an evidence using Mathematica for smaller graphs among them for n>55. The problem for the case n=7 remains open, however, it is highly likely that it would be realized as a principal graph, thanks to numerical computation by Ikeda.
We construct the quantum s-tuple subfactors for an AFD II_1 subfactor with finite index and depth, for an arbitrary natural number s. This is a generalization of the quantum multiple subfactors by J.Erlijman and H.Wenzl, which generalizes the quantum double construction of a subfactor for the case that the original subfactor gives rise to a braided tensor category. In this paper we give a multiple construction for a subfactor with a weaker condition than braidedness of the bimodule system.
We introduce a new skein module for three manifolds based on properly embedded surfaces and their relations introduced by D.Bar-Natan, and modified by M.Khovanov. We compute the structure of the modules for some manifolds, including Seifert fibred manifolds.