Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Casselman-Jacquet functor   We study the Casselman-Jacquet functor $J$, viewed as a functor from the
(derived) category of $(\mathfrak{g},K)$-modules to the (derived) category of
$(\mathfrak{g},N^-)$-modules, $N^-$ is the negative maximal unipotent. We give
a functorial definition of $J$ as a certain right adjoint functor, and identify
it as a composition of two averaging functors $\text{Av}^{N^-}_!\circ
\text{Av}^N_*$. We show that it is also isomorphic to the composition
$\text{Av}^{N^-}_*\circ \text{Av}^N_!$. Our key tool is the pseudo-identity
functor that acts on the (derived) category of (twisted) $D$-modules on an
algebraic stack.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph