, Volume 47, Issue 11, pp 1115-1122

Double quantization on the coadjoint representation of sl(n)

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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 \(\mathfrak{g}*\) .