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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/2512.24317 |
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| _version_ | 1866908740729438208 |
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| author | Sheu, Nai-Heng |
| author_facet | Sheu, Nai-Heng |
| contents | Given a group $G$ and $V$ a representation of $G$, denote the number of indecomposable summands of $V^{\otimes k}$ by $b_k^{G, V}$. Given a tilting representation $T$ of $\text{SL}_2(K)$ where $K=\overline{K}$ and of characteristic $p>2$, we show that $Ck^{-α_p}(\text{dim} T)^k<b_k^{T, \text{SL}_2(K)}<Dk^{-α_p}(\text{dim} T)^k$ for some $C, D>0$ where $α_p=1-(1/2)\log_p(\frac{p+1}{2}).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24317 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractal behavior of tensor powers of tilting modules of $\text{SL}_2$ Sheu, Nai-Heng Representation Theory Given a group $G$ and $V$ a representation of $G$, denote the number of indecomposable summands of $V^{\otimes k}$ by $b_k^{G, V}$. Given a tilting representation $T$ of $\text{SL}_2(K)$ where $K=\overline{K}$ and of characteristic $p>2$, we show that $Ck^{-α_p}(\text{dim} T)^k<b_k^{T, \text{SL}_2(K)}<Dk^{-α_p}(\text{dim} T)^k$ for some $C, D>0$ where $α_p=1-(1/2)\log_p(\frac{p+1}{2}).$ |
| title | Fractal behavior of tensor powers of tilting modules of $\text{SL}_2$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2512.24317 |