Modular representation theory of algebras associated with complex reflection groups

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We studied about modular representation theory of cyclotomic Hecke algebras and cyclotomic q-Schur algebras associated with the complex reflection groups of type G(r, 1, n). In the modular representation theory, it is one of the important problems to determine the character of modules. We described the character of Weyl modules of cyclotomic q-Schur algebras by using some combinatorics. We also defined induction and restriction functors. By using these functors, we showed that module categories of cyclotomic q-Schur algebras categorify the Fock space.