Double quantization on the coadjoint representation of sl(n)

Abstract

For $\g=sl(n)$ we construct a two parametric $U_h(\g)$-invariant family of algebras, $(S\g)_{t,h}$, which defines a quantization of the function algebra $S\g$ on the coadjoint representation and in the parameter $t$ gives a quantization of the Lie bracket. The family induces a two parametric deformation of the function algebra of any maximal orbit which is a quantization of the Kirillov-Kostant-Souriau bracket in the parameter $t$. In addition we construct a quantum de Rham complex on $\g^*$.