Quantization and reduction for torsion free CR manifolds
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913767540916224 |
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| author | Galasso, Andrea Hsiao, Chin-Yu |
| author_facet | Galasso, Andrea Hsiao, Chin-Yu |
| contents | Consider a compact torsion free CR manifold $X$ and assume that $X$ admits a compact CR Lie group action $G$. Let $L$ be a $G$-equivariant rigid CR line bundle over $X$. It seems natural to consider the space of $G$-invariant CR sections in the high tensor powers as quantization space, on which a certain weighted $G$-invariant Fourier-Szegő operator projects. Under certain natural assumptions, we show that the group invariant Fourier-Szegő projector admits a full asymptotic expansion. As an application, if the tensor power of the line bundle is large enough, we prove that quantization commutes with reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00478 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantization and reduction for torsion free CR manifolds Galasso, Andrea Hsiao, Chin-Yu Complex Variables Differential Geometry Symplectic Geometry Consider a compact torsion free CR manifold $X$ and assume that $X$ admits a compact CR Lie group action $G$. Let $L$ be a $G$-equivariant rigid CR line bundle over $X$. It seems natural to consider the space of $G$-invariant CR sections in the high tensor powers as quantization space, on which a certain weighted $G$-invariant Fourier-Szegő operator projects. Under certain natural assumptions, we show that the group invariant Fourier-Szegő projector admits a full asymptotic expansion. As an application, if the tensor power of the line bundle is large enough, we prove that quantization commutes with reduction. |
| title | Quantization and reduction for torsion free CR manifolds |
| topic | Complex Variables Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2411.00478 |