The Whittaker Modules For The Schr(?)dinger Algebra S(2)

In this paper, the Whittaker modules for the Schrodinger algebra S(2) are aimed to study. First, we give the definition of the Whittaker modules for S(2), and construct the Whittaker modules Mψ and Lψ,ξ Then we determine the Whittaker vectors of Mψ and Lψ,ξ respectively. We show that Lψ,ξ is irreducible if ψ is non-singular. Finally, we construct a family of modules Mψ,ξ which are similar as Whittaker modules. We give the sufficient and necessary conditions for Mψ,ξ to be irreducible.