Whittaker modules for the derivation Lie algebra of torus with two variables

Abstract

Let $\mathcal{L}$ be the derivation Lie algebra of $\mathbb{C}[t_1^{\pm 1},t_2^{\pm 1}]$. Given a triangle decomposition $\mathcal{L}={\mathcal{L}}^{+}\oplus \mathfrak{h}\oplus {\mathcal{L}}^{-}$, we define a nonsingular Lie algebra homomorphism $\psi :{\mathcal{L}}^{+}\to \mathbb{C}$ and the universal Whittaker $\mathcal{L}$-module $W_{\psi }$ of type $\psi$. We obtain all Whittaker vectors and submodules of $W_{\psi }$, and all simple Whittaker $\mathcal{L}$-modules of type $\psi$.

14 pages

References in corpus (1)

• Tensor product weight modules over the Virasoro algebra