Abstract: In this talk, I'll describe the tools needed to construct the irreducible representations of a generic Hecke algebra that specializes to the group algebra of the reflection group G(b,1,2). The tools include b-partitions of 2, specializations, specialized algebras, Hecke algebras and generic algebras. I'll discuss the interplay between these various notions and how they fit into the construction of the irreducible representations. Finally, I'll present results which construct the irreducible representations of the generic Hecke algebra.