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arXiv · 2512.18877

Schurian-finiteness of blocks of type B Hecke algebras

Susumu Ariki·Sinéad Lyle·Liron Speyer·Qi Wang
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Abstract

Schurian-finiteness, also known as $\tau$-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.

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Susumu Ariki, Sinéad Lyle, Liron Speyer, Qi Wang. 2025-12-21. Schurian-finiteness of blocks of type B Hecke algebras. https://arxiv.org/abs/2512.18877

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