Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Whittaker modules for the planar Galilean conformal algebra and its
  central extension   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 $\phi$, where
$\phi:\mathcal{G}^{+}=\widetilde{\mathcal{G}}^{+}\longrightarrow\mathbb{C}$ 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 $\phi$ is irreducible if and only if $\phi$ 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.

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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg