Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Berezin form on symmetric $R$-spaces and reflection positivity   For a symmetric $R$-space $K/L=G/P$ the standard intertwining operators
provide a canonical $G$-invariant pairing between sections of line bundles over
$G/P$ and its opposite $G/\overline{P}$. Twisting this pairing with an
involution of $G$ which defines a non-compactly causal symmetric space $G/H$ we
obtain an $H$-invariant form on sections of line bundles over $G/P$.
Restricting to the open $H$-orbits in $G/P$ constructs the Berezin forms
studied previously by G. van Dijk, S. C. Hille and V. F. Molchanov. We
determine for which $H$-orbits in $G/P$ and for which line bundles the Berezin
form is positive semidefinite, and in this case identify the corresponding
representations of the dual group $G^c$ as unitary highest weight
representations. We further relate this procedure of passing from
representations of $G$ to representations of $G^c$ to reflection positivity.

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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex