Conformally Equivariant Quantization - a Complete Classification
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...
Збережено в:
Видавець: | Інститут математики НАН України |
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Дата: | 2012 |
Автор: | |
Формат: | Стаття |
Мова: | English |
Опубліковано: |
Інститут математики НАН України
2012
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Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148414 |
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Цитувати: | Conformally Equivariant Quantization - a Complete Classification / Jean-Philippe Michel // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 25 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of UkraineРезюме: | 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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