Cellularity of endomorphism algebras of tilting objects
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866908823541776384 |
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| author | Bellamy, Gwyn Thiel, Ulrich |
| author_facet | Bellamy, Gwyn Thiel, Ulrich |
| contents | We show that, in a highest weight category with duality, the endomorphism algebra of a tilting object is naturally a cellular algebra. Our proof generalizes a recent construction of Andersen, Stroppel, and Tubbenhauer. This result raises the question of whether all cellular algebras can be realized in this way. The construction also works without the presence of a duality and yields standard bases, in the sense of Du and Rui, which have similar combinatorial features to cellular bases. As an application, we obtain standard bases -- and thus a general theory of "cell modules" -- for Hecke algebras associated to finite complex reflection groups (as introduced by Broué, Malle, and Rouquier) via category $\mathcal{O}$ of the rational Cherednik algebra. For real reflection groups these bases are cellular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_07887 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Cellularity of endomorphism algebras of tilting objects Bellamy, Gwyn Thiel, Ulrich Representation Theory We show that, in a highest weight category with duality, the endomorphism algebra of a tilting object is naturally a cellular algebra. Our proof generalizes a recent construction of Andersen, Stroppel, and Tubbenhauer. This result raises the question of whether all cellular algebras can be realized in this way. The construction also works without the presence of a duality and yields standard bases, in the sense of Du and Rui, which have similar combinatorial features to cellular bases. As an application, we obtain standard bases -- and thus a general theory of "cell modules" -- for Hecke algebras associated to finite complex reflection groups (as introduced by Broué, Malle, and Rouquier) via category $\mathcal{O}$ of the rational Cherednik algebra. For real reflection groups these bases are cellular. |
| title | Cellularity of endomorphism algebras of tilting objects |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2107.07887 |