Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Segal-Bargmann Transform on Classical Matrix Lie Groups   We study the complex-time Segal-Bargmann transform
$\mathbf{B}_{s,\tau}^{K_N}$ on a compact type Lie group $K_N$, where $K_N$ is
one of the following classical matrix Lie groups: the special orthogonal group
$\mathrm{SO}(N,\mathbb{R})$, the special unitary group $\mathrm{SU}(N)$, or the
compact symplectic group $\mathrm{Sp}(N)$. Our work complements and extends the
results of Driver, Hall, and Kemp on the Segal-Bargman transform for the
unitary group $\mathrm{U}(N)$. We provide an effective method of computing the
action of the Segal-Bargmann transform on \emph{trace polynomials}, which
comprise a subspace of smooth functions on $K_N$ extending the polynomial
functional calculus. Using these results, we show that as $N\to\infty$, the
finite-dimensional transform $\mathbf{B}_{s,\tau}^{K_N}$ has a meaningful limit
$\mathscr{G}_{s,\tau}^{(\beta)}$ (where $\beta$ is a parameter associated with
$\mathrm{SO}(N,\mathbb{R})$, $\mathrm{SU}(N)$, or $\mathrm{Sp}(N)$), which can
be identified as an operator on the space of complex Laurent polynomials.

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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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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: ao-sci