Quantum symmetric spaces Original Research Article

Let G be a semisimple Lie group, g its Lie algebra. For any symmetric space M over G we construct a new (deformed) multiplication in the space A of smooth functions on M. This multiplication is invariant under the action of the Drinfeld-Jimbo quantum group Uhg and is commutative with respect to an involutive operator image. Such a multiplication is unique. Let M be a kählerian symmetric space with the canonical Poisson structure. Then we construct a Uhg-invariant multiplication in A which depends on two parameters and is a quantization of that structure.