Conjugate pairs of Hadamard subfactors and vertex models
Abstract
We show that any two Hadamard subfactors arising from a pair of distinct complex Hadamard matrices of order 3 are either equal or conjugate by a unitary in the relative commutant of their intersection. Moreover, when the Hadamard subfactors are not equal, we prove the factoriality of their intersection, and it turns out to be a vertex model subfactor. We compute the first relative commutant and characterize this subfactor by identifying it with a particular type of Krishnan-Sunder subfactor. A few key invariants, including the Pimsner-Popa probabilistic number, the angle, and the Connes-St{\o}rmer relative entropy for the pair of Hadamard subfactors are computed to understand their relative position.
Keywords
Cite
@article{arxiv.2401.01664,
title = {Conjugate pairs of Hadamard subfactors and vertex models},
author = {Keshab Chandra Bakshi and Satyajit Guin and Guruprasad},
journal= {arXiv preprint arXiv:2401.01664},
year = {2025}
}
Comments
Referee's suggestions incorporated, to appear in Proc. Indian Acad. Sci. Math. Sci