  These are notes prepared for ICRA workshop at Torun, Poland, August 2007. In
the first part, we explain results on canonical basic sets by Geck and Jacon
and propose a categorification framework which is suitable for our example of
Hecke algebras. In the second part, we review basics of Kashiwara crystal and
explain the Fock space theory of cyclotomic Hecke algebras and its
applications. In the third part, we explain Rouquier's theory of
quasihereditary covers of cyclotomic Hecke algebras. We add detailed
explanation of the proofs here. The third part is based on my intensive course
given at Nagoya university in January 2007.
