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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.08020 |
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| _version_ | 1866916037411209216 |
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| author | Weng, Daping |
| author_facet | Weng, Daping |
| contents | We introduce weighted cycles on weaves of general Dynkin types and define a skew-symmetrizable intersection pairing between weighted cycles. We prove that weighted cycles on a weave form a Laurent polynomial algebra and construct a quantization for this algebra using the skew-symmetric intersection pairing in the simply-laced case. We define merodromies along weighted cycles as functions on the decorated flag moduli space of the weave. We relate weighted cycles with cluster variables in a cluster algebra and prove that mutations of weighted cycles are compatible with mutations of cluster variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted Cycles on Weaves Weng, Daping Representation Theory 13F60, 22E46, 05C38, 14M15, 57K31, 81R60 We introduce weighted cycles on weaves of general Dynkin types and define a skew-symmetrizable intersection pairing between weighted cycles. We prove that weighted cycles on a weave form a Laurent polynomial algebra and construct a quantization for this algebra using the skew-symmetric intersection pairing in the simply-laced case. We define merodromies along weighted cycles as functions on the decorated flag moduli space of the weave. We relate weighted cycles with cluster variables in a cluster algebra and prove that mutations of weighted cycles are compatible with mutations of cluster variables. |
| title | Weighted Cycles on Weaves |
| topic | Representation Theory 13F60, 22E46, 05C38, 14M15, 57K31, 81R60 |
| url | https://arxiv.org/abs/2503.08020 |