Verma modules for finite W-algebras

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The ultimate aim of this project is to determine the finite dimensional simple modules for finite W-algebras. Finite W-algebras occur in the study of infinite dimensionalrepresentations of complex semisimple Lie algebras and also in mathematical physics. Further, the representation theory of finite W-algebras has connections to the representation theory of quantum groups and cyclotomic Hecke algebras. We intend to define Verma modules for finite W-algebras, which have simple heads and such that each finite dimensional simple module occurs as one of these heads.