CALCULATING THE p-CANONICAL BASIS OF HECKE ALGEBRAS.

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 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. [ABSTRACT FROM AUTHOR]