Strict quantization of coadjoint orbits
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For every semisimple coadjoint orbit O^ of a complex connected semisimple Lie group G^, we obtain a family of G^-invariant products ∗^ℏ on the space of holomorphic functions on O^. For every semisimple coadjoint orbit O of a real connected semisimple Lie group G, we obtain a family of G-invariant products ∗ℏ on a space A(O) of certain analytic functions on O by restriction. A(O), endowed with one of the products ∗ℏ, is a G-Fréchet algebra, and the formal expansion of the products around ℏ=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.
Original language | English |
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Journal | Journal of Noncommutative Geometry |
Volume | 15 |
Issue number | 4 |
Pages (from-to) | 1181-1249 |
ISSN | 1661-6952 |
DOIs | |
Publication status | Published - 2021 |
- Formal deformation quantization, strict quantization, coadjoint orbits, Verma modules, Shapovalov pairing, Stein manifolds
Research areas
ID: 290040903