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arXiv · 2506.14351

A noncommutative construction of families of biunitary matrices and application to subfactors

Keshab Chandra Bakshi·Satyajit Guin·Guruprasad
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Abstract

We introduce a construction that, given a pair (u,v) of complex Hadamard matrices of the same order, generates infinitely many biunitary matrices of varying (and distinct) orders. As a key application, this framework yields nested sequences of vertex model subfactors that are not a tower of downward basic construction. Notably, the construction is noncommutative: interchanging the matrices (i.e., considering (v,u) instead of (u,v)) can lead to non-isomorphic subfactors. Focusing on the Hadamard equivalence class of the Fourier matrix, we provide a full characterization of the resulting vertex model subfactors, along with explicit computations of their relative commutants. Along the way, we conduct a detailed study of certain naturally arising inner and outer automorphisms that play a key role in the structure of these subfactors.

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Keshab Chandra Bakshi, Satyajit Guin, Guruprasad. 2025-06-17. A noncommutative construction of families of biunitary matrices and application to subfactors. https://arxiv.org/abs/2506.14351

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