Commutativity of quantization with conic reduction for torus actions on compact CR manifolds
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866910560544620544 |
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| author | Galasso, Andrea |
| author_facet | Galasso, Andrea |
| contents | We define conic reduction $X^{\mathrm{red}}_ν$ for torus actions on the boundary $X$ of a strictly pseudo-convex domain and for a given weight $ν$ labeling a unitary irreducible representation. There is a natural residual circle action on $X^{\mathrm{red}}_ν$. We have two natural decompositions of the corresponding Hardy spaces $H(X)$ and $H(X^{\mathrm{red}}_ν)$. The first one is given by the ladder of isotypes $H(X)_{kν}$, $k\in\mathbb{Z}$, the second one is given by the $k$-th Fourier components $H(X^{\mathrm{red}}_ν)_k$ induced by the residual circle action. The aim of this paper is to prove that they are isomorphic for $k$ sufficiently large. The result is given for spaces of $(0,q)$-forms with $L^2$-coefficient when $X$ is a CR manifold with non-degenerate Levi-curvature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2110_07104 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Commutativity of quantization with conic reduction for torus actions on compact CR manifolds Galasso, Andrea Complex Variables Symplectic Geometry We define conic reduction $X^{\mathrm{red}}_ν$ for torus actions on the boundary $X$ of a strictly pseudo-convex domain and for a given weight $ν$ labeling a unitary irreducible representation. There is a natural residual circle action on $X^{\mathrm{red}}_ν$. We have two natural decompositions of the corresponding Hardy spaces $H(X)$ and $H(X^{\mathrm{red}}_ν)$. The first one is given by the ladder of isotypes $H(X)_{kν}$, $k\in\mathbb{Z}$, the second one is given by the $k$-th Fourier components $H(X^{\mathrm{red}}_ν)_k$ induced by the residual circle action. The aim of this paper is to prove that they are isomorphic for $k$ sufficiently large. The result is given for spaces of $(0,q)$-forms with $L^2$-coefficient when $X$ is a CR manifold with non-degenerate Levi-curvature. |
| title | Commutativity of quantization with conic reduction for torus actions on compact CR manifolds |
| topic | Complex Variables Symplectic Geometry |
| url | https://arxiv.org/abs/2110.07104 |