Tensor powers of representations of (diagram) monoids
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866915430406291456 |
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| author | He, David Tubbenhauer, Daniel |
| author_facet | He, David Tubbenhauer, Daniel |
| contents | We study tensor powers of representations of finite monoids, focusing on the growth behavior of their composition length and the number of indecomposable summands. Special attention is given to diagram monoids such as the Temperley-Lieb, Motzkin, and Brauer monoids. For these examples, we compute explicit data, including some character tables, and analyze patterns in the decomposition of their tensor powers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04054 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor powers of representations of (diagram) monoids He, David Tubbenhauer, Daniel Representation Theory Category Theory Group Theory Primary: 05A16, 20M30, Secondary: 18M05, 20M20 We study tensor powers of representations of finite monoids, focusing on the growth behavior of their composition length and the number of indecomposable summands. Special attention is given to diagram monoids such as the Temperley-Lieb, Motzkin, and Brauer monoids. For these examples, we compute explicit data, including some character tables, and analyze patterns in the decomposition of their tensor powers. |
| title | Tensor powers of representations of (diagram) monoids |
| topic | Representation Theory Category Theory Group Theory Primary: 05A16, 20M30, Secondary: 18M05, 20M20 |
| url | https://arxiv.org/abs/2508.04054 |