2025/12/21 by Susumu Ariki, Sinéad Lyle, Ariki, Susumu +5
Mathematics · Computer Science · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #semigroups and automata theory
paper · doi:10.48550/arxiv.2512.18877
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.