I'm interested in the cohomology ring $H^*(G/B)$ of a flag variety $G/B$, where $G$ is a complex semi-simple Lie group and $B$ the Borel subgroup. Borel (1953) showed that this ring is isomorphic to the coinvariants algebra of the associated root system. $H^*(G/B)$ also has a distinguished basis given by Schubert cells. Demazure (1974) and Bernstein, Gelfand, Gelfand (1973) identified elements of the coinvariants algebra corresponding to the Schubert cells.

I know that flag varieties play an important role in representation theory (Borel-Weil-Bott theorem, for instance). I'd like to know whether the cohomology ring $H^*(G/B)$ carries any useful representation-theoretic information. References to literature would also be very appreciated.