On deformation quantizations of symplectic supervarieties

Abstract

We classify deformation quantizations of the symplectic supervarieties that are smooth and admissible. This generalizes the corresponding result of Bezrukavnikov and Kaledin to the super case. We relate the equivalence classes of quantizations of supervarieties with that of their even reduced symplectic varieties. Finally, we prove that certain nilpotent orbits of basic Lie superalgebras are admissible and split, and classify their deformation quantizations.

arXiv comment21 pages/V2 The language has been improved, and some typos have been corrected. V3: Revised version responding to reviewer's comments. Some errors are corrected