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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:
**R**^{x} in **C**^{x} is a split form of
*GL*_{1}, but
*S*^{1} in **C**^{x} is not.

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** Previous:** 5.ii. Rational Functions with Real
Critical Points