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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2512.17830 |
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| _version_ | 1866915758399815680 |
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| author | Martin, Paul P. Rowell, Eric C. Torzewska, Fiona |
| author_facet | Martin, Paul P. Rowell, Eric C. Torzewska, Fiona |
| contents | We first motivate the study of a certain quotient of the loop braid category, both for the mathematics underpinning recent approaches to topological quantum computation; and as a key example in non-semisimple higher representation theory. For reasons that will become clear, we call this quotient the mixed doubles category, $MD$. Then our main result is a theorem classifying all mixed doubles representations in rank-2.
Each representation yields a mixed doubles group representation for every loop braid group $LB_n$, and we are able to analyse the unified linear representation theory of many of these sequences of representations, using a mixture of very classical, classical, and new techniques. In particular this is a motivating example for the `glue' generalisation of charge-conserving representation theory (a form of rigid higher non-semisimplicity) introduced recently. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Paravortices: loop braid representations with both generators involutive Martin, Paul P. Rowell, Eric C. Torzewska, Fiona Quantum Algebra We first motivate the study of a certain quotient of the loop braid category, both for the mathematics underpinning recent approaches to topological quantum computation; and as a key example in non-semisimple higher representation theory. For reasons that will become clear, we call this quotient the mixed doubles category, $MD$. Then our main result is a theorem classifying all mixed doubles representations in rank-2. Each representation yields a mixed doubles group representation for every loop braid group $LB_n$, and we are able to analyse the unified linear representation theory of many of these sequences of representations, using a mixture of very classical, classical, and new techniques. In particular this is a motivating example for the `glue' generalisation of charge-conserving representation theory (a form of rigid higher non-semisimplicity) introduced recently. |
| title | Paravortices: loop braid representations with both generators involutive |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2512.17830 |