Schurian-finiteness of blocks of type B Hecke algebras
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908727305568256 |
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| author | Ariki, Susumu Lyle, Sinéad Speyer, Liron Wang, Qi |
| author_facet | Ariki, Susumu Lyle, Sinéad Speyer, Liron Wang, Qi |
| contents | Schurian-finiteness, also known as $τ$-tilting finiteness, is equivalent to the finiteness of various representation theoretic objects such as wide subcategories. The first three authors classified Schurian-finite blocks of type A Hecke algebras in [ALS23]. Here we study the Schurian-finiteness of blocks of type B Hecke algebras, and determine the Schurian-finiteness of all blocks if the Hecke algebra is `non-integral', and for almost all blocks in the integral case. The only remaining cases are a small number of blocks in defect $3$ when $e=3$, and a family of blocks in defects $3$ and $4$ for $e\geqslant4$. The classification is mostly achieved by methods using decomposition numbers, with many degenerate cases requiring direct study using standard methods from the representation theory of quivers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schurian-finiteness of blocks of type B Hecke algebras Ariki, Susumu Lyle, Sinéad Speyer, Liron Wang, Qi Representation Theory Rings and Algebras Schurian-finiteness, also known as $τ$-tilting finiteness, is equivalent to the finiteness of various representation theoretic objects such as wide subcategories. The first three authors classified Schurian-finite blocks of type A Hecke algebras in [ALS23]. Here we study the Schurian-finiteness of blocks of type B Hecke algebras, and determine the Schurian-finiteness of all blocks if the Hecke algebra is `non-integral', and for almost all blocks in the integral case. The only remaining cases are a small number of blocks in defect $3$ when $e=3$, and a family of blocks in defects $3$ and $4$ for $e\geqslant4$. The classification is mostly achieved by methods using decomposition numbers, with many degenerate cases requiring direct study using standard methods from the representation theory of quivers. |
| title | Schurian-finiteness of blocks of type B Hecke algebras |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2512.18877 |