  We present a simple proof of a strengthening of the derived
Beilinson-Bernstein localization theorem using the formalism of descent in
derived algebraic geometry. The arguments and results apply to arbitrary
modules without the need to fix infinitesimal character. Roughly speaking, we
demonstrate that all Ug-modules are the invariants, or equivalently
coinvariants, of the action of intertwining functors (a refined form of Weyl
group symmetry). This is a quantum version of descent for the
Grothendieck-Springer simultaneous resolution. In an appendix we present an
alternative perspective, which identifies the descent data in both classical
and quantum versions as a categorical action of Demazure operators.

Representation Theory;Algebraic Geometry;Quantum Algebra