The blocks of the \(q\)-Schur algebra
Results which give a partial determination of the blocks of the \(q\)-Schur algebra at roots of unity have previously been obtained by the author (for \(n=2\)), by James and Mathas (for \(n\geq d\)) and by Thams. The main result of this paper is to determine such blocks completely from the blocks of a suitable quantum general linear group, thus generalizing a result of Donkin on classical Schur algebras. The methods used involve playing the Dipper-Donkin quantization against the Manin quantization, and finding a suitable generalization of Andersen's strong linkage principle. This allows Donkins' original argument to be lifted to the quantum case. Note that \(\inf_K^H(V)\) in the statement of Proposition 4.5 should read \(\text{ind}_K^H(V)\).
scientific article; zbMATH DE number 1213859