A noncommutative construction of families of biunitary matrices and application to subfactors
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912824265015296 |
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| author | Bakshi, Keshab Chandra Guin, Satyajit Guruprasad |
| author_facet | Bakshi, Keshab Chandra Guin, Satyajit Guruprasad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A noncommutative construction of families of biunitary matrices and application to subfactors Bakshi, Keshab Chandra Guin, Satyajit Guruprasad Operator Algebras Functional Analysis 46L37, 46L55 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. |
| title | A noncommutative construction of families of biunitary matrices and application to subfactors |
| topic | Operator Algebras Functional Analysis 46L37, 46L55 |
| url | https://arxiv.org/abs/2506.14351 |