Cellularity of KLR and weighted KLRW algebras via crystals
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917545173319680 |
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| author | Mathas, Andrew Tubbenhauer, Daniel |
| author_facet | Mathas, Andrew Tubbenhauer, Daniel |
| contents | We prove that the weighted KLRW algebras of finite type, and their cyclotomic quotients, are cellular algebras. The cellular bases are explicitly described using crystal graphs. As a special case, this proves that the KLR algebras of finite type are cellular. As one application, we give explicit formulas for the graded decomposition numbers of the cyclotomic algebras in level one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_13867 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cellularity of KLR and weighted KLRW algebras via crystals Mathas, Andrew Tubbenhauer, Daniel Representation Theory Combinatorics Rings and Algebras Primary 18M30, 20C08, Secondary 05E10, 17B10, 18N25 We prove that the weighted KLRW algebras of finite type, and their cyclotomic quotients, are cellular algebras. The cellular bases are explicitly described using crystal graphs. As a special case, this proves that the KLR algebras of finite type are cellular. As one application, we give explicit formulas for the graded decomposition numbers of the cyclotomic algebras in level one. |
| title | Cellularity of KLR and weighted KLRW algebras via crystals |
| topic | Representation Theory Combinatorics Rings and Algebras Primary 18M30, 20C08, Secondary 05E10, 17B10, 18N25 |
| url | https://arxiv.org/abs/2309.13867 |