English

On deformation quantizations of symplectic supervarieties

Representation Theory 2026-03-05 v3

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.

Keywords

Cite

@article{arxiv.2407.19450,
  title  = {On deformation quantizations of symplectic supervarieties},
  author = {Husileng Xiao},
  journal= {arXiv preprint arXiv:2407.19450},
  year   = {2026}
}

Comments

21 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

R2 v1 2026-06-28T17:55:50.170Z