Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1181-1249 |
| Seitenumfang | 69 |
| Fachzeitschrift | Journal of Noncommutative Geometry |
| Jahrgang | 15 |
| Ausgabenummer | 4 |
| Frühes Online-Datum | 15 Dez. 2021 |
| Publikationsstatus | Veröffentlicht - Dez. 2021 |
Abstract
For every semisimple coadjoint orbit O y of a complex connected semisimple Lie group G y, we obtain a family of G-invariant products * h„ on the space of holomorphic functions on O y. For every semisimple coadjoint orbit O of a real connected semisimple Lie group G, we obtain a family of G-invariant products * h on a space A.O/of certain analytic functions on O by restriction. A.O/, endowed with one of the products * h„, is a G-Fréchet algebra, and the formal expansion of the products around h = 0 determines a formal deformation quantization of O, which is of Wick type if G is compact. Our construction relies on an explicit computation of the canonical element of the Shapovalov pairing between generalized Verma modules and complex analytic results on the extension of holomorphic functions.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Geometrie und Topologie
- Mathematik (insg.)
- Algebra und Zahlentheorie
- Mathematik (insg.)
- Mathematische Physik
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in: Journal of Noncommutative Geometry, Jahrgang 15, Nr. 4, 12.2021, S. 1181-1249.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Strict quantization of coadjoint orbits
AU - Schmitt, Philipp Lothar
N1 - Funding Information: Funding. Research supported by the Danish National Research Foundation through the Centre of Symmetry and Deformation (DNRF92).
PY - 2021/12
Y1 - 2021/12
N2 - For every semisimple coadjoint orbit O y of a complex connected semisimple Lie group G y, we obtain a family of G-invariant products * h„ on the space of holomorphic functions on O y. For every semisimple coadjoint orbit O of a real connected semisimple Lie group G, we obtain a family of G-invariant products * h on a space A.O/of certain analytic functions on O by restriction. A.O/, endowed with one of the products * h„, is a G-Fréchet algebra, and the formal expansion of the products around h = 0 determines a formal deformation quantization of O, which is of Wick type if G is compact. Our construction relies on an explicit computation of the canonical element of the Shapovalov pairing between generalized Verma modules and complex analytic results on the extension of holomorphic functions.
AB - For every semisimple coadjoint orbit O y of a complex connected semisimple Lie group G y, we obtain a family of G-invariant products * h„ on the space of holomorphic functions on O y. For every semisimple coadjoint orbit O of a real connected semisimple Lie group G, we obtain a family of G-invariant products * h on a space A.O/of certain analytic functions on O by restriction. A.O/, endowed with one of the products * h„, is a G-Fréchet algebra, and the formal expansion of the products around h = 0 determines a formal deformation quantization of O, which is of Wick type if G is compact. Our construction relies on an explicit computation of the canonical element of the Shapovalov pairing between generalized Verma modules and complex analytic results on the extension of holomorphic functions.
KW - Coadjoint orbits
KW - Formal deformation quantization
KW - Shapovalov pairing
KW - Stein manifolds
KW - Strict quantization
KW - Verma modules
UR - http://www.scopus.com/inward/record.url?scp=85123253625&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1907.03185
DO - 10.48550/arXiv.1907.03185
M3 - Article
VL - 15
SP - 1181
EP - 1249
JO - Journal of Noncommutative Geometry
JF - Journal of Noncommutative Geometry
SN - 1661-6952
IS - 4
ER -