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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.22985 |
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| _version_ | 1866908736750092288 |
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| author | Larsen, Michael J. |
| author_facet | Larsen, Michael J. |
| contents | Given a finite-dimensional faithful representation $V$ of a linearly reductive group $G$ over a field $K=\bar K$, we consider the growth of the number of irreducible factors of $V^{\otimes n}$ when $n$ is large. We prove that there exist upper and lower bounds which are constant multiples of $n^{-u/2} (\dim V)^n$, where $u$ is the dimension of any maximal unipotent subgroup of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22985 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor Power Asymptotics for Linearly Reductive Groups Larsen, Michael J. Representation Theory 17B10 (Primary) 20G05, 60B15, 60J15 (Secondary) Given a finite-dimensional faithful representation $V$ of a linearly reductive group $G$ over a field $K=\bar K$, we consider the growth of the number of irreducible factors of $V^{\otimes n}$ when $n$ is large. We prove that there exist upper and lower bounds which are constant multiples of $n^{-u/2} (\dim V)^n$, where $u$ is the dimension of any maximal unipotent subgroup of $G$. |
| title | Tensor Power Asymptotics for Linearly Reductive Groups |
| topic | Representation Theory 17B10 (Primary) 20G05, 60B15, 60J15 (Secondary) |
| url | https://arxiv.org/abs/2512.22985 |