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2006 Experimentation and Conjectures in the Real Schubert Calculus for Flag Manifolds
Jim Ruffo, Yuval Sivan, Evgenia Soprunova, Frank Sottile
Experiment. Math. 15(2): 199-222 (2006).


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 the conjecture in some special cases using discriminants and establish relationships between different cases of the conjecture.


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Jim Ruffo. Yuval Sivan. Evgenia Soprunova. Frank Sottile. "Experimentation and Conjectures in the Real Schubert Calculus for Flag Manifolds." Experiment. Math. 15 (2) 199 - 222, 2006.


Published: 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1111.14049
MathSciNet: MR2253007

Primary: 14M15 , 14N15 , 14P99

Keywords: flag manifold , Grassmannian , Schubert variety , Shapiro conjecture

Rights: Copyright © 2006 A K Peters, Ltd.

Vol.15 • No. 2 • 2006
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