Seidai Yasuda

On Haagerup’s List of Potential Principal Graphs of Subfactors

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.

Harmonic and equianharmonic equations in the Grothendieck–Teichmüller group. III

We study behaviours of the ‘equianharmonic’ parameter of the Grothendieck–Teichmuller group introduced by Lochak and Schneps. Using geometric construction of a certain one-parameter family of quartics, we realize the Galois action on the fundamental group of a punctured Mordell elliptic curve in the standard Galois action on a specific subgroup of the braid group B4. A consequence is to represent a matrix specialization of the ‘equianharmonic’ parameter in terms of special values of the adelic beta function introduced and studied by Anderson and Ihara.

Non-negativity of the Fourier Coefficients of Eta Products Associated to Regular Systems of Weights

We prove Saito’s conjecture [9, Conjecture 13.5] about the non-negativity of the Fourier coecients of the eta products associated to regular systems of weights.