Whittaker modules for the Schrodinger-Virasoro algebra

In this paper, Whittaker modules for the Schrodinger-Virasoro algebra $mathfrak{sv}$ are defined. The Whittaker vectors and the irreducibility of the Whittaker modules are studied. $mathfrak{sv}$ has a triangular decomposition according to the Cartan algebra $mathfrak{h}:$ $$mathfrak{sv}=mathfrak{sv}^{-}oplusmathfrak{h}oplusmathfrak{sv}^{+}.$$ For any Lie algebra homomorphism $psi:mathfrak{sv}^{+}tomathbb{C}$, we can define Whittaker modules of type $psi.$ When $psi$ is nonsingular, the Whittaker vectors, the irreducibility and the classification of Whittaker modules are completely determined. When $psi$ is singular, by constructing some special Whittaker vectors, we find that the Whittaker modules are all reducible. Moreover, we get some more precise results for special $psi$.