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arXiv · 2401.01664

Conjugate pairs of Hadamard subfactors and vertex models

Keshab Chandra Bakshi·Satyajit Guin·Guruprasad
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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.

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Keshab Chandra Bakshi, Satyajit Guin, Guruprasad. 2024-01-03. Conjugate pairs of Hadamard subfactors and vertex models. https://arxiv.org/abs/2401.01664

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