Twisted Graded Hecke Algebras For Elementary Abelian Groups

Twisted graded Hecke algebras were introduced by S. Witherspoon as a common generalization of graded Hecke algebras and twisted symplectic reflection algebras. In this thesis, the structure and representation theory of twisted graded Hecke algebras for elementary abelian groups are studied. Such an algebra A is finitely generated as a module over its center. Moreover, for a generic central character X, there exists a unique simple A-module on which the center acts by X.