Coxeter embeddings are injective
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917646414381056 |
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| author | Elias, Ben Heng, Edmund |
| author_facet | Elias, Ben Heng, Edmund |
| contents | We show that certain embeddings of Coxeter groups within other Coxeter groups are injective using the notion of Coxeter partitions. Moreover, we study Lusztig's partitions, which are generalizations of Lusztig's admissible maps and Crisp's foldings. We show that they classify the simplest type of Coxeter partitions, whose embeddings of Coxeter groups send each generator to a product of commuting generators. Consequently, these embeddings are also injective, and we prove that they preserve Coxeter numbers. These results were previously known, due to work of Mühlherr and Dyer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coxeter embeddings are injective Elias, Ben Heng, Edmund Group Theory Representation Theory 20F55, 20C08 We show that certain embeddings of Coxeter groups within other Coxeter groups are injective using the notion of Coxeter partitions. Moreover, we study Lusztig's partitions, which are generalizations of Lusztig's admissible maps and Crisp's foldings. We show that they classify the simplest type of Coxeter partitions, whose embeddings of Coxeter groups send each generator to a product of commuting generators. Consequently, these embeddings are also injective, and we prove that they preserve Coxeter numbers. These results were previously known, due to work of Mühlherr and Dyer. |
| title | Coxeter embeddings are injective |
| topic | Group Theory Representation Theory 20F55, 20C08 |
| url | https://arxiv.org/abs/2402.00974 |