Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tube domains and restrictions of minimal representations   In this paper we study the restrictions of the minimal representation in the
analytic continuation of the scalar holomorphic discrete series from
$Sp(n,\mathbb{R})$ to $GL(n,\mathbb{R})$, and from SU(n,n) to
$GL(n,\mathbb{C})$ respectively. We work with the realisations of the
representation spaces as $L^2$-spaces on the boundary orbits of rank one of the
corresponding cones, and give explicit integral operators that play the role of
the intertwining operators for the decomposition. We prove inversion formulas
for dense subspaces and use them to prove the Plancherel theorem for the
respective decomposition. The Plancherel measure turns out to be absolutely
continuous with respect to the Lebesgue measure in both cases.

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The categories of this paper are: q-bio
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
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The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
1
The categories of this paper are: cs