4.iii. Further extensions of the Schubert calculus

This special Schubert calculus admits further extensions, some of which are known to be fully real. Interestingly, some problems involving the Lagrangian Grassmannian 4.ii.e are known to be fully unreal, a new phenomenon. Further investigation is encouraged; in particular, the Lagrangian Schubert calculus may yield the first class of enumerative which are not fully real.

1. General Schubert calculus
2. Quantum Schubert calculus
3. Schubert calculus of flags
4. Reality in the orthogonal Schubert calculus
5. Unreality in the Lagrangian Schubert calculus