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On the decomposition matrices of the quantized Schur algebra

arXiv:math/9803023

Abstract

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.

AMS-tex, 30 pages