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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.00278 |
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| _version_ | 1866910392576376832 |
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| author | Cuntz, Michael Mühlherr, Bernhard |
| author_facet | Cuntz, Michael Mühlherr, Bernhard |
| contents | Dimitrov and Fioresi introduced an object that they call a generalized root system. This is a finite set of vectors in a euclidean space satisfying certain compatibilities between angles and sums and differences of elements. They conjecture that every generalized root system is equivalent to one associated to a restriction of a Weyl arrangement. In this note we prove the conjecture and provide a complete classification of generalized root systems up to equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00278 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A classification of generalized root systems Cuntz, Michael Mühlherr, Bernhard Combinatorics Quantum Algebra Representation Theory 17B22, 52C35, 16T30 Dimitrov and Fioresi introduced an object that they call a generalized root system. This is a finite set of vectors in a euclidean space satisfying certain compatibilities between angles and sums and differences of elements. They conjecture that every generalized root system is equivalent to one associated to a restriction of a Weyl arrangement. In this note we prove the conjecture and provide a complete classification of generalized root systems up to equivalence. |
| title | A classification of generalized root systems |
| topic | Combinatorics Quantum Algebra Representation Theory 17B22, 52C35, 16T30 |
| url | https://arxiv.org/abs/2404.00278 |