Conformally Equivariant Quantization - a Complete Classification
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
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Conformally Equivariant Quantization - a Complete Classification
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| Creator |
Michel, Jean-Philippe
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| Description |
Conformally equivariant quantization is a peculiar map between symbols of real weight δ and differential operators acting on tensor densities, whose real weights are designed by λ and λ+δ. The existence and uniqueness of such a map has been proved by Duval, Lecomte and Ovsienko for a generic weight δ. Later, Silhan has determined the critical values of δ for which unique existence is lost, and conjectured that for those values of δ existence is lost for a generic weight λ. We fully determine the cases of existence and uniqueness of the conformally equivariant quantization in terms of the values of δ and λ. Namely, (i) unique existence is lost if and only if there is a nontrivial conformally invariant differential operator on the space of symbols of weight δ, and (ii) in that case the conformally equivariant quantization exists only for a finite number of λ, corresponding to nontrivial conformally invariant differential operators on λ-densities. The assertion (i) is proved in the more general context of IFFT (or AHS) equivariant quantization.
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| Date |
2019-02-18T11:56:51Z
2019-02-18T11:56:51Z 2012 |
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| Type |
Article
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| Identifier |
Conformally Equivariant Quantization - a Complete Classification / Jean-Philippe Michel // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 25 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 53A55; 53A30; 17B56; 47E05 DOI: http://dx.doi.org/10.3842/SIGMA.2012.022 http://dspace.nbuv.gov.ua/handle/123456789/148414 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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