QUANTIZED ALGEBRAS OF FUNCTIONS ON HOMOGENEOUS SPACES WITH POISSON STABILIZERS

摘要: Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K closed Poisson-Lie subgroup, 0 < q 1. We study quantization C(Gq/Kq) of the algebra continuous functions on G/K. Using results Soibelman and Dijkhuizen-Stokman we classify irreducible representations obtain composition series for C(Gq/Kq). describe closures symplectic leaves G/K refining well-known description in case flag manifolds terms Bruhat order. then show that same rules topology spectrum Next family C*-algebras C(Gq/Kq), ≤ 1, has canonical structure field provides strict deformation \({\mathbb{C}[G/K]}\) . Finally, extending result Nagy, is canonically KK-equivalent to C(G/K).