Experimentation and Conjectures in the Real Schubert Calculus for Flag Manifolds
Experimentation and Conjectures in the Real Schubert Calculus for Flag Manifolds
The Shapiro conjecture in the real Schubert calculus, while likely true for Grassmannians, fails to hold for flag manifolds, but in a very interesting way. We give a refinement of the Shapiro conjecture for flag manifolds and present massive computational experimentation in support of this refined conjecture. We also prove …