Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916810307141632 |
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| author | Galasso, Andrea |
| author_facet | Galasso, Andrea |
| contents | The asymptotic results for Berezin-Toeplitz operators yield a strict quantization for the algebra of smooth functions on a given Hodge manifold. It seems natural to generalize this picture for quantizable pseudo-Kähler manifolds in presence of a group action. Thus, in this setting we introduce a Berezin transform which has a complete asymptotic expansion on the preimage of the zero set of the moment map. It leads in a natural way to prove that certain quantization maps are strict. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03322 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions Galasso, Andrea Symplectic Geometry The asymptotic results for Berezin-Toeplitz operators yield a strict quantization for the algebra of smooth functions on a given Hodge manifold. It seems natural to generalize this picture for quantizable pseudo-Kähler manifolds in presence of a group action. Thus, in this setting we introduce a Berezin transform which has a complete asymptotic expansion on the preimage of the zero set of the moment map. It leads in a natural way to prove that certain quantization maps are strict. |
| title | Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2410.03322 |