Double quantization on the coadjoint representation of sl(n)

Abstract

For $\mathfrak{g} = sl(n)$ we construct a two parametric $U_h (\mathfrak{g})$-invariant family of algebras, $(S\mathfrak{g})_{t,h}$, that is a quantization of the function algebra $S\mathfrak{g}$ on the coadjoint representation. Along the parameter t the family gives a quantization of the Lie bracket. This family induces a two parametric $U_h (\mathfrak{g})$-invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-Souriau bracket. Yet we construct a quantum de Rham complex on $\mathfrak{g}*$.