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 Uhβg and is
commutative with respect to an involutive operator S~:AβAβAβA. Such a multiplication is unique. Let M be a k\"{a}hlerian
symmetric space with the canonical Poisson structure. Then we construct a
Uhβg-invariant multiplication in A which depends on two parameters
and is a quantization of that structure.Comment: 16 pp, LaTe