Whittaker modules for the Schrödinger-Virasoro algebra

Abstract

In this paper, Whittaker modules for the Schrödinger-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 $\mathfrak{h}:$ $$\mathfrak{sv}={\mathfrak{sv}}^{-}\oplus \mathfrak{h}\oplus {\mathfrak{sv}}^{+}.$$ For any Lie algebra homomorphism $\psi :{\mathfrak{sv}}^{+}\to \mathbb{C}$, 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 $\psi$.

22 pages

References in corpus (1)

• The derivation algebra and automorphism group of the twisted Schrödinger-Virasoro algebra

Cited by in corpus (4)

• Whittaker Modules For The W-algebra W(2,2)
• Whittaker modules for a Lie algebra of Block type
• Blocks and modules for Whittaker pairs
• Whittaker Modules for Graded Lie Algebras