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Recently Tewari and van Willigenburg constructed modules of the 0-Heckealgebra that are mapped to the quasisymmetric Schur functions by thequasisymmetric characteristic and decomposed them into a direct sum of certainsubmodules. We show that these submodules are indecomposable by determiningtheir endomorphism rings.

The decomposition of 0-Hecke modules associated to quasisymmetric Schur functions