Corpus ID: 119677205

Quantizations of conical symplectic resolutions II: category $\mathcal O$ and symplectic duality

  title={Quantizations of conical symplectic resolutions II: category \$\mathcal O\$ and symplectic duality},
  author={T. Braden and Anthony Licata and N. Proudfoot and B. Webster},
  journal={arXiv: Representation Theory},
We define and study category $\mathcal O$ for a symplectic resolution, generalizing the classical BGG category $\mathcal O$, which is associated with the Springer resolution. This includes the development of intrinsic properties parallelling the BGG case, such as a highest weight structure and analogues of twisting and shuffling functors, along with an extensive discussion of individual examples. We observe that category $\mathcal O$ is often Koszul, and its Koszul dual is often equivalent to… Expand