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## Generalizations of Conjecture 5.1

The Grassmannian, flag manifolds, and Lagrangian Grassmannian are examples of flag varieties G/P where G is a reductive algebraic group and P is a parabolic subgroup. These flag varieties have Schubert varieties and the most general form of the Schubert calculus involves zero-dimensional intersections of these Schubert varieties. Likewise, these flag varieties have real forms (given by split§ forms of G and P) and there is a generalization of Conjecture 5.1 for these real forms. This generalization is false, but in a very interesting way. We describe what is known about this general conjecture for the manifolds of partial flags, the orthogonal Grassmannian, and the Lagrangian Grassmannian, and give conjectures describing what we believe to be true.

Subsections
§Split is a technical term: Rx in Cx is a split form of GL1, but S1 in Cx is not.

Next: 6. Lower Bounds in The Schubert Calculus