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.
Originalsprog | Engelsk |
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Tidsskrift | Journal of Noncommutative Geometry |
Vol/bind | 15 |
Udgave nummer | 4 |
Sider (fra-til) | 1181-1249 |
ISSN | 1661-6952 |
DOI | |
Status | Udgivet - 2021 |
ID: 290040903