Uh(g) invariant quantization of coadjoint orbits and vector bundles over them
✍ Scribed by Joseph Donin
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 199 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0393-0440
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✦ Synopsis
Let M be a coadjoint semisimple orbit of a simple Lie group G. Let U h (g) be a quantum group corresponding to G. We construct a universal family of U h (g) invariant quantizations of the sheaf of functions on M and describe all such quantizations. We also describe all two parameter U h (g) invariant quantizations on M, which can be considered as U h (g) invariant quantizations of the Kirillov-Kostant-Souriau (KKS) Poisson bracket on M. We also consider how those quantizations relate to the natural polarizations of M with respect to the KKS bracket. Using polarizations, we quantize the sheaves of sections of vector bundles on M as one-and two-sided U h (g) invariant modules over a quantized function sheaf.