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RELATIVE POSITION BETWEEN A PAIR OF SPIN MODEL SUBFACTORS
Published online by Cambridge University Press: 10 March 2025
Abstract
Jones [‘Two subfactors and the algebraic decomposition of bimodules over 
$II_1$ factors’, Acta Math. Vietnam 33(3) (2008), 209–218] proposed the study of ‘two subfactors’ of a 
$II_1$ factor as a quantization of two closed subspaces in a Hilbert space. Motivated by this, we initiate a systematic study of a special class of two subfactors, namely a pair of spin model subfactors. We characterize which pairs of distinct complex Hadamard matrices in 
$M_n(\mathbb {C})$ give rise to distinct spin model subfactors. Then, a detailed investigation is carried out for 
$n=2$, where the spin model subfactors correspond to 
$\mathbb {Z}_2$-actions on the hyperfinite type 
$II_1$ factor R. We observe that the intersection of the pair of spin model subfactors in this case is a nonirreducible vertex model subfactor and we characterize it as a diagonal subfactor. A few key invariants for the pair of spin model subfactors are computed to understand their relative positions.
Keywords
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- Research Article
- Information
- Copyright
- © The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
Communicated by Aidan Sims
The first author acknowledges the support of INSPIRE Faculty grant DST/INSPIRE/04/2019/002754 and the second author acknowledges the support of SERB grant MTR/2021/000818.
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