The article posted in the comment is pretty comprehensive and nice.

The immediate reason this theorem is useful for my research is the proof of the Kazhdan-Lusztig Conjecture. Specifically, using the realization of representations of reductive Lie algebras as modules over (twisted) sheaves of differential operators on a flag variety $G/B$. The Kazhdan-Lusztig conjecture establishes a correspondence between the representations of an algebraic group $G$, to the algebraic-geometric structure of generalized flag varieties $G/B$. In particular, it gives the relation between the characters of Verma modules of Lie algebras and the intersection cohomology on the Schubert varieties.

The article posted in the comment is pretty comprehensive and nice.

The immediate reason this theorem is useful for my research is the proof of the Kazhdan-Lusztig Conjecture. Specifically, using the realization of representations of reductive Lie algebras as modules over (twisted) sheaves of differential operators on a flag variety $G/B$. The Kazhdan-Lusztig conjecture establishes a correspondence between the representations of an algebraic group $G$, to the algebraic-geometric structure of generalized flag varieties $G/B$. In particular, it gives the relation between the characters of Verma modules of Lie algebras and the intersection cohomology on the Schubert varieties.