Asymptotic Growth of Trivial Summands in Tensor Powers
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917120419299328 |
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| author | Sheu, Nai-Heng |
| author_facet | Sheu, Nai-Heng |
| contents | Given a finite-dimensional representation $V$ over an algebraically closed field of an abstract group $G$, we consider the number of the trivial summand counted with multiplicity in the direct sum decomposition of $V^{\otimes n}$. We give necessary and sufficient conditions when the field is of characteristic $0$ and when the field is of characteristic $p$ so that $(V^{\otimes n})_n$ has a subsequence $(V^{\otimes n_k})_k$ such that $V^{\otimes n_k}$ contains enough trivial summands when $k$ is sufficiently large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic Growth of Trivial Summands in Tensor Powers Sheu, Nai-Heng Representation Theory Given a finite-dimensional representation $V$ over an algebraically closed field of an abstract group $G$, we consider the number of the trivial summand counted with multiplicity in the direct sum decomposition of $V^{\otimes n}$. We give necessary and sufficient conditions when the field is of characteristic $0$ and when the field is of characteristic $p$ so that $(V^{\otimes n})_n$ has a subsequence $(V^{\otimes n_k})_k$ such that $V^{\otimes n_k}$ contains enough trivial summands when $k$ is sufficiently large. |
| title | Asymptotic Growth of Trivial Summands in Tensor Powers |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2501.11125 |