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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Abstract

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

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

Dates
First available in Project Euclid: 5 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.em/1175789741

Mathematical Reviews number (MathSciNet)
MR2253007

Zentralblatt MATH identifier
1111.14049

Subjects
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

Keywords
Shapiro conjecture Schubert variety Grassmannian flag manifold

Citation

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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