Growth Problems of Quantum Groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911257524699136 |
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| author | O'Sullivan, Jensen Tubbenhauer, Daniel |
| author_facet | O'Sullivan, Jensen Tubbenhauer, Daniel |
| contents | We study the asymptotic size of decompositions of tensor powers of tilting modules for quantum groups (mostly at a complex root of unity). In type A1 we obtain a sharp result for the number of indecomposable summands, explained by a one dimensional half-line random walk with a periodic congruence constraint. In general type we prove a universal law: the dominant part is governed only by the dimension of the module, while the correction depends only on the root system, so the asymptotic size is largely independent of the specific tilting module. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Growth Problems of Quantum Groups O'Sullivan, Jensen Tubbenhauer, Daniel Representation Theory Combinatorics Quantum Algebra Primary: 17B37, 18M05, Secondary: 05A15, 16T05 We study the asymptotic size of decompositions of tensor powers of tilting modules for quantum groups (mostly at a complex root of unity). In type A1 we obtain a sharp result for the number of indecomposable summands, explained by a one dimensional half-line random walk with a periodic congruence constraint. In general type we prove a universal law: the dominant part is governed only by the dimension of the module, while the correction depends only on the root system, so the asymptotic size is largely independent of the specific tilting module. |
| title | Growth Problems of Quantum Groups |
| topic | Representation Theory Combinatorics Quantum Algebra Primary: 17B37, 18M05, Secondary: 05A15, 16T05 |
| url | https://arxiv.org/abs/2511.06737 |