Experimental Mathematics

Experimentation and Conjectures in the Real Schubert Calculus for Flag Manifolds

Jim Ruffo, Yuval Sivan, Evgenia Soprunova, and Frank Sottile

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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.

Article information

Experiment. Math., Volume 15, Issue 2 (2006), 199-222.

First available in Project Euclid: 5 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14N15: Classical problems, Schubert calculus 14P99: None of the above, but in this section

Shapiro conjecture Schubert variety Grassmannian flag manifold


Ruffo, Jim; Sivan, Yuval; Soprunova, Evgenia; Sottile, Frank. Experimentation and Conjectures in the Real Schubert Calculus for Flag Manifolds. Experiment. Math. 15 (2006), no. 2, 199--222. https://projecteuclid.org/euclid.em/1175789741

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