Eigenfunction asymptotics in the complex domain for a compact Lie group
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911124108083200 |
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| author | Gallivanone, Simone Paoletti, Roberto |
| author_facet | Gallivanone, Simone Paoletti, Roberto |
| contents | Let $(G,κ)$ be a compact connected Lie group endowed with a biinvariant Riemannian metric, and let $\tilde{G}$ be the complexification of $G$. We apply Grauert tube techniques to the near-diagonal scaling asymptotics of certain operator kernels, which are defined in terms of the matrix elements of an irreducuble representation drifting to infinity along a ray in weight space. These kernels are the equivariant components of Poisson and Szegő kernels on a fixed sphere bundle in $\tilde{G}$, when the latter is identified with the tangent bundle of $G$ in an appropriate way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigenfunction asymptotics in the complex domain for a compact Lie group Gallivanone, Simone Paoletti, Roberto Symplectic Geometry Let $(G,κ)$ be a compact connected Lie group endowed with a biinvariant Riemannian metric, and let $\tilde{G}$ be the complexification of $G$. We apply Grauert tube techniques to the near-diagonal scaling asymptotics of certain operator kernels, which are defined in terms of the matrix elements of an irreducuble representation drifting to infinity along a ray in weight space. These kernels are the equivariant components of Poisson and Szegő kernels on a fixed sphere bundle in $\tilde{G}$, when the latter is identified with the tangent bundle of $G$ in an appropriate way. |
| title | Eigenfunction asymptotics in the complex domain for a compact Lie group |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2507.18285 |