On the decomposition matrices of the quantized Schur algebra
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algebraconjecturedecompositionschurapproachbasescanonicaldimension
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We prove the decomposition conjecture of Leclerc and Thibon for the Schur algebra. We also give a new approach to the Lusztig conjecture for the dimension of the simple U(sl_k)-modules at roots of unity via canonical bases of the Hall algebra.
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