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- W4223651757 abstract "We describe an algorithm for computing the $p$-canonical basis of the Hecke algebra, or one of its antispherical modules. The algorithm does not operate in the Hecke category directly, but rather uses a faithful embedding of the Hecke category inside a semisimple category to build a model for indecomposable objects and bases of their morphism spaces. Inside this semisimple category, objects are sequences of Coxeter group elements, and morphisms are (sparse) matrices over a fraction field, making it quite amenable to computations. This strategy works for the full Hecke category over any base field, but in the antispherical case we must instead work over $mathbb{Z}_{(p)}$ and use an idempotent lifting argument to deduce the result for a field of characteristic $p > 0$. We also describe a less sophisticated algorithm which is much more suited to the case of finite groups. We provide complete implementations of both algorithms in the MAGMA computer algebra system." @default.
- W4223651757 created "2022-04-15" @default.
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- W4223651757 date "2022-04-11" @default.
- W4223651757 modified "2023-09-26" @default.
- W4223651757 title "Calculating the $p$-canonical basis of Hecke algebras" @default.
- W4223651757 doi "https://doi.org/10.48550/arxiv.2204.04924" @default.
- W4223651757 hasPublicationYear "2022" @default.
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