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We generalize Soergel's tilting algorithm to singular weights and deduce fromthis the validity of the Lascoux-Leclerc-Thibon conjecture on the connectionbetween the canonical basis of the basic submodule of the Fock module and therepresentation theory of the Hecke-algebras at root of unity.

The Lascoux, Leclerc and Thibon algorithm and Soergel's tilting algorithm