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<p>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–Størmer relative entropy for the pair of Hadamard subfactors are computed to understand their relative position.</p>

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Conjugate pairs of Hadamard subfactors and vertex models

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Keshab Chandra Bakshi,
  • Satyajit Guin,
  • Guruprasad

摘要

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–Størmer relative entropy for the pair of Hadamard subfactors are computed to understand their relative position.