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We study the quantizations of the algebras of regular functions on nilpotentorbits. We show that such a quantization always exists and is unique if theorbit is birationally rigid. Further we show that, for special birationallyrigid orbits, the quantization has integral central character in all cases butfour (one orbit in E_7 and three orbits in E_8). We use this to complete thecomputation of Goldie ranks for primitive ideals with integral centralcharacter for all special nilpotent orbits but one (in E_8). Our mainingredient is results on the geometry of normalizations of the closures ofnilpotent orbits by Fu and Namikawa.

Quantizations of regular functions on nilpotent orbits