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- W4297267140 abstract "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 $Ntoinfty$, 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." @default.
- W4297267140 created "2022-09-28" @default.
- W4297267140 creator A5056848846 @default.
- W4297267140 date "2018-09-22" @default.
- W4297267140 modified "2023-09-23" @default.
- W4297267140 title "The Segal-Bargmann Transform on Classical Matrix Lie Groups" @default.
- W4297267140 doi "https://doi.org/10.48550/arxiv.1809.08465" @default.
- W4297267140 hasPublicationYear "2018" @default.
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