Susumu Ariki
Published 2009-03-20, updated 2011-03-02Version 3
Generalizing recent work of Brundan and Kleshchev, we introduce grading on Dipper-James' $q$-Schur algebra, and prove a graded analogue of the Leclerc and Thibon's conjecture on the decomposition numbers of the $q$-Schur algebra when $q^2\neq1$ and $q^3\neq1$.
Comments: 25 pages, (v2) added details of the proof, (v3) have changed notations to standard ones and corrected various confusions
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