  We re-examine some topics in representation theory of Lie algebras and
Springer theory in a more general context, viewing the universal enveloping
algebra as an example of the section ring of a quantization of a conical
symplectic resolution. While some modification from this classical context is
necessary, many familiar features survive. These include a version of the
Beilinson-Bernstein localization theorem, a theory of Harish-Chandra bimodules
and their relationship to convolution operators on cohomology, and a discrete
group action on the derived category of representations, generalizing the braid
group action on category O via twisting functors.
  Our primary goal is to apply these results to other quantized symplectic
resolutions, including quiver varieties and hypertoric varieties. This provides
a new context for known results about Lie algebras, Cherednik algebras, finite
W-algebras, and hypertoric enveloping algebras, while also pointing to the
study of new algebras arising from more general resolutions.
