Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions
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 the presence of a group action. Thus, in this setting, we introduce...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/213528 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions. Andrea Galasso. SIGMA 21 (2025), 048, 25 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862655720393015296 |
|---|---|
| author | Galasso, Andrea |
| author_facet | Galasso, Andrea |
| citation_txt | Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions. Andrea Galasso. SIGMA 21 (2025), 048, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 the 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 proving that certain quantization maps are strict.
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| first_indexed | 2026-03-15T20:34:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213528 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T20:34:39Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Galasso, Andrea 2026-02-18T11:25:48Z 2025 Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions. Andrea Galasso. SIGMA 21 (2025), 048, 25 pages 1815-0659 2020 Mathematics Subject Classification: 32V20; 32A25; 53D50 arXiv:2410.03322 https://nasplib.isofts.kiev.ua/handle/123456789/213528 https://doi.org/10.3842/SIGMA.2025.048 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 the 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 proving that certain quantization maps are strict. We are indebted to the referees for various interesting comments and for suggesting several improvements. The author thanks Chin-Yu Hsiao and Herrmann Hendrik for their valuable conversations. The author is a member of GNSAGA, part of the Istituto Nazionale di Alta Matematica, and expresses gratitude to the group for its support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions Article published earlier |
| spellingShingle | Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions Galasso, Andrea |
| title | Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions |
| title_full | Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions |
| title_fullStr | Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions |
| title_full_unstemmed | Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions |
| title_short | Strict Quantization for Compact Pseudo-Kähler Manifolds and Group Actions |
| title_sort | strict quantization for compact pseudo-kähler manifolds and group actions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213528 |
| work_keys_str_mv | AT galassoandrea strictquantizationforcompactpseudokahlermanifoldsandgroupactions |