论文标题
惠特克（Whittaker
Whittaker modules for the planar Galilean conformal algebra and its central extension
论文作者
论文摘要
令$ \ mathcal {g} $为平面galilean conformal代数，$ \ widetilde {\ mathcal {g}} $是其通用中心扩展。然后$ \ MATHCAL {G} $（resp。 $ \ MATHCAL {G} = \ MATHCAL {G}^{+} \ OPLUS \ MATHCAL {G}^{0} \ oplus \ Mathcal \ Mathcal {G}^{ - } $（resp。 $ \ widetilde {\ Mathcal {g}} = \ widetilde {\ Mathcal {g}}}^{+} \ oplus \ oplus \ widetilde {\ Mathcal {g}}}}^{0}^{0} \ oplus \ wideTilde在本文中，我们研究了通用和通用的Whittaker $ \ MATHCAL {G} $ - 模块（分别$ ϕ：\ MATHCAL {g}^{+} = \ widetilde {\ Mathcal {g}}}^{+} \ longrightArrow \ Mathbb {c} $是一个lie代数同源。我们对通用和通用惠特克模块的同构类别进行分类。此外，我们表明$ ϕ $的通用惠特克模块在且仅当$ ϕ $非发挥时是不可约的。对于非语言情况，我们完全确定了通用和通用惠特克模块中的惠特克载体。对于奇异案例，我们构建了一些适当的通用惠特克模块的基本模块。
Let $\mathcal{G}$ be the planar Galilean conformal algebra and $\widetilde{\mathcal{G}}$ be its universal central extension. Then $\mathcal{G}$ (resp. $\widetilde{\mathcal{G}}$) admits a triangular decomposition: $\mathcal{G}=\mathcal{G}^{+}\oplus\mathcal{G}^{0}\oplus\mathcal{G}^{-}$ (resp. $\widetilde{\mathcal{G}}=\widetilde{\mathcal{G}}^{+}\oplus\widetilde{\mathcal{G}}^{0}\oplus\widetilde{\mathcal{G}}^{-}$). In this paper, we study universal and generic Whittaker $\mathcal{G}$-modules (resp. $\widetilde{\mathcal{G}}$-modules) of type $ϕ$, where $ϕ:\mathcal{G}^{+}=\widetilde{\mathcal{G}}^{+}\longrightarrow\mathbb{C}$ is a Lie algebra homomorphism. We classify the isomorphism classes of universal and generic Whittaker modules. Moreover, we show that a generic Whittaker modules of type $ϕ$ is irreducible if and only if $ϕ$ is nonsingular. For the nonsingular case, we completely determine the Whittaker vectors in universal and generic Whittaker modules. For the singular case, we concretely construct some proper submodules of generic Whittaker modules.
