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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rational functions and real Schubert calculus


Authors: A. Eremenko, A. Gabrielov, M. Shapiro and A. Vainshtein
Journal: Proc. Amer. Math. Soc. 134 (2006), 949-957
MSC (2000): Primary 14P05; Secondary 26C15
Published electronically: July 25, 2005
MathSciNet review: 2196025
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Abstract: We single out some problems of Schubert calculus of subspaces of codimension $2$that have the property that all their solutions are real whenever the data are real. Our arguments explore the connection between subspaces of codimension $2$and rational functions of one variable.


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Additional Information

A. Eremenko
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
Email: eremenko@math.purdue.edu

A. Gabrielov
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
Email: agabriel@math.purdue.edu

M. Shapiro
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: mshapiro@math.msu.edu

A. Vainshtein
Affiliation: Department of Computer Science, University of Haifa, Mount Carmel, 31905 Haifa, Israel
Email: alek@cs.haifa.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08048-2
PII: S 0002-9939(05)08048-2
Received by editor(s): August 25, 2004
Received by editor(s) in revised form: October 29, 2004
Published electronically: July 25, 2005
Additional Notes: The authors were supported by NSF grants DMS-0100512 and DMS-0244421 (A.E.), DMS-0200861 and DMS-0245628 (A.G.), and DMS-0401178 (M.S.); and by the BSF grant 2002375 (M.S.\ and A.V.) and by the Institute of Quantum Science, MSU (M.S.).
Communicated by: John R. Stembridge
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.