For geometric representation theorists down here.

Consider the Beilinson-Bernstein theorem:

Functor of global sections establishes the correspondence between twisted D-modules with fixed twist θ on the flag variety and g-representations with fixed central character. These are modules over the same algebra D[θ] = U /(Z −χ). This correspondence respects the structure of abelian category. It takes K-equivariant D-modules to (g, K)-admissible modules.

Why do people refer to its derived version as the Koszul duality?

How is this related to Soergel's conjecture?

(please tag: geometric-representation-theory, homological-algebra, koszul-duality)

For geometric representation theorists down here.

Consider the Beilinson-Bernstein theorem:

Functor of global sections establishes the correspondence between twisted D-modules with fixed twist θ on the flag variety and g-representations with fixed central character. These are modules over the same algebra D[θ] = U /(Z −χ). This correspondence respects the structure of abelian category. It takes K-equivariant D-modules to (g, K)-admissible modules.

Why do people refer to its derived version as the Koszul duality?

How is this related to Soergel's conjecture?

(please tag: geometric-representation-theory, homological-algebra, koszul-duality)