Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poles of the Standard $\mathcal{L}$-function of $G_2$ and the
  Rallis-Schiffmann Lift   We characterize the cuspidal representations of $G_2$ whose standard
$\mathcal{L}$-function admits a pole at $s=2$ as the image of Rallis-Schiffmann
lift for the commuting pair $\left(\widetilde{SL_2}, G_2\right)$ in
$\widetilde{Sp_{14}}$. The image consists of non-tempered representations. The
main tool is the recent construction, by the second author, of a family of
Rankin-Selberg integrals representing the standard $\mathcal{L}$-function.

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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int