numerically effective cotangent bundle; degree root systems; connected reductive algebraic group; projective variety; Borel subgroups; line bundles; orbits; tangent bundle; Weyl group; maximal tori; \(\ell\)-adic cohomology groups; virtual representation; characters; irreducible representations; multiplicities; irreducible components; intersection cohomology; Schubert cells; Weyl groups; Hecke algebras; enveloping algebras; complex reductive Lie algebras; unipotent representations 