Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morita's Theory for the Symplectic Groups   We construct and study the holomorphic discrete series representation and the
principal series representation of the symplectic group $\mathrm{Sp}(2n,F)$
over a $p$-adic field $F$ as well as a duality between some sub-representations
of these two representations. The constructions of these two representations
generalize those defined in Morita and Murase's works. Moreover, Morita built a
duality for $\mathrm{SL}(2, F)$ defined by residues. We view the duality we
defined as an algebraic interpretation of Morita's duality in some extent and
its generalization to the symplectic groups.

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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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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: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex