In the previous chapter, we studied the representation theory of binary Schur algebras in the combinatorial language of coloured Pascal triangles. The central problem of modular representation theory is to extend this analysis to more general algebraic objects, such as symmetric groups, (non-binary) Schur algebras, Hecke categories, as well as objects which are beyond the realms of this book (such as finite groups of Lie type, Lie algebras, Kac–Moody algebras, and quantum groups). Of course, this requires a suitably rich combinatorial language to replace our earlier use of coloured Pascal triangles; this new language is provided by Kazhdan–Lusztig theory.