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Quantizations of Regular Functions on Nilpotent Orbits
by Ivan Loseu

Vol. 13 No. 2 (2018) P.199~P.225
 DOI: https://doi.org/10.21915/BIMAS.2018202 10.21915/BIMAS.2018202

ABSTRACT

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

KEYWORDS
Nilpotent orbit, quantization, primitive ideal, W-algebra.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 17B35 ; secondary: 53D55, 16G99.

MILESTONES