Quantizations of Regular Functions on Nilpotent Orbits
Vol. 13 No. 2 (2018) P.199~P.225
DOI: || https://doi.org/10.21915/BIMAS.2018202 |
| ||10.21915/BIMAS.2018202 |
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.
Nilpotent orbit, quantization, primitive ideal, W-algebra.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 17B35 ; secondary: 53D55, 16G99.
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Revised : 2016-06-30