Moving vectors and core blocks of Ariki-Koike algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917949669900288 |
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| author | Li, Yanbo Qi, Xiangyu Tan, Kai Meng |
| author_facet | Li, Yanbo Qi, Xiangyu Tan, Kai Meng |
| contents | We classify the core blocks of Ariki-Koike algebras by their moving vectors. Using this classification, we obtain a necessary and sufficient condition for Scopes equivalence between two core blocks, and express the number of simple modules lying in a core block as a classical Kostka number. Under certain conditions on the multicharge and moving vector, we further relate the graded decomposition numbers of these blocks in characteristic zero with the graded decomposition numbers of the Iwahori-Hecke algebras of type $A$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_12725 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moving vectors and core blocks of Ariki-Koike algebras Li, Yanbo Qi, Xiangyu Tan, Kai Meng Representation Theory 20C08, 05E10 We classify the core blocks of Ariki-Koike algebras by their moving vectors. Using this classification, we obtain a necessary and sufficient condition for Scopes equivalence between two core blocks, and express the number of simple modules lying in a core block as a classical Kostka number. Under certain conditions on the multicharge and moving vector, we further relate the graded decomposition numbers of these blocks in characteristic zero with the graded decomposition numbers of the Iwahori-Hecke algebras of type $A$. |
| title | Moving vectors and core blocks of Ariki-Koike algebras |
| topic | Representation Theory 20C08, 05E10 |
| url | https://arxiv.org/abs/2502.12725 |