Details
| Original language | English |
|---|---|
| Pages (from-to) | 1181-1249 |
| Number of pages | 69 |
| Journal | Journal of Noncommutative Geometry |
| Volume | 15 |
| Issue number | 4 |
| Early online date | 15 Dec 2021 |
| Publication status | Published - Dec 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.
Keywords
- Coadjoint orbits, Formal deformation quantization, Shapovalov pairing, Stein manifolds, Strict quantization, Verma modules
ASJC Scopus subject areas
- Mathematics(all)
- Geometry and Topology
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Mathematical Physics
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In: Journal of Noncommutative Geometry, Vol. 15, No. 4, 12.2021, p. 1181-1249.
Research output: Contribution to journal › Article › Research › 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 -