Whittaker modules for the Schrödinger–Witt algebra

In this paper, Whittaker modules for the Schrödinger–Witt algebra sv are defined. The Whittaker vectors and the irreducibility of the Whittaker modules are studied. sv has a triangular decomposition according to its Cartan subalgebra h: sv=sv−⊕h⊕sv+. For any Lie algebra homomorphism ψ:sv+→C, we can define Whittaker modules of type ψ. When ψ is nonsingular, the Whittaker vectors, the irreducibility, and the classification of Whittaker modules are completely determined. When ψ 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 ψ.