Decomposition matrices for category o of rational cherednik algebras

We find the decomposition matrices of the Category O for rational Cherednik algebras of Coxeter groups of types H4, F4, E6, E7 and E8. The decomposition matrix is an important numerical invariant of the Category O: the matrix entries are the multiplicities of irreducible modules in standard modules (also called Verma modules). In the case of F4, E6, E7 and E8, the parameter is not a half-integer and for E8 we only consider the blocks of defect 2. In the case of F4, we consider the case of equal parameters only. As a consequence, we obtain character formulas for irreducible representations in the Category O, as well as a classification of the finite-dimensional representations of these rational Cherednik algebras.