Method of quantum characters in equivariant quantization

Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose Ah(M) is a Uh(g)-equivariant quantization of the function algebra A(M) on M . We develop a method of restricting Ah(M) to the Uh(g)-equivariant quantization on Gorbits in M . We are concerned with those quantizations that may be simultaneously represented as subalgebras in U∗ h(g) and quotients of Ah(M). It turns out that they are in one-to-one correspondence with characters of the algebra Ah(M). We specialize our approach to the situation g = gl(n,C), M = End(Cn), and Ah(M) the so-called reflection equation algebra associated with the representation of Uh(g) on Cn. For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and bisymmetric orbits. We build a two-parameter deformation family and obtain, as a limit case, the U(g)-equivariant quantization of the KirillovKostant-Souriau bracket on symmetric orbits.