The second paper of Kazhdan and Lusztig established a geometric setting for definition of Kazhdan–Lusztig polynomials, namely, the geometry of singularities of Schubert varieties in the flag variety. Much of the later work of Lusztig explored analogues of Kazhdan–Lusztig polynomials in the context of other natural singular algebraic varieties arising in representation theory, in particular, closures of nilpotent orbits and quiver varieties.
In their second paper, Kazhdan and Lusztig introduced a geometric approach to define Kazhdan–Lusztig polynomials, concentrating on the geometry of Schubert varieties' singularities within flag varieties. Subsequent work by Lusztig examined similar polynomials in other natural singular algebraic varieties that arise in representation theory, such as closures of nilpotent orbits and quiver varieties.