I should know what is expected to be true, and what is the story.

I should also know what is known to be true, i.e. proven. And I should know how the proof goes.

I should also know what is known to be false, and counter examples.

For our flag variety, why is it true that, $T$-equivariant homology and $G$-equivariant homology only differ by Weyl covering.