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Injectivity of Generalized Wronski Maps

Published online by Cambridge University Press:  20 November 2018

Yanhe Huang ,
Frank Sottile  and
Igor Zelenko
Yanhe Huang
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA e-mail: yanhe_huang@berkeley.edu
Frank Sottile
Affiliation:
Department of Mathematics, Texas A & M University, College Station, Texas 77843, USA e-mail: sottile@math.tamu.eduzelenko@math.tamu.edu
Igor Zelenko
Affiliation:
Department of Mathematics, Texas A & M University, College Station, Texas 77843, USA e-mail: sottile@math.tamu.eduzelenko@math.tamu.edu
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Abstract

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We study linear projections on Plücker space whose restriction to the Grassmannian is a non-trivial branched cover. When an automorphism of the Grassmannian preserves the fibers, we show that the Grassmannian is necessarily of $m$-dimensional linear subspaces in a symplectic vector space of dimension $2m$, and the linear map is the Lagrangian involution. The Wronski map for a self-adjoint linear diòerential operator and the pole placement map for symmetric linear systems are natural examples.

Keywords

14M1534A3093B55Wronski mapPlücker embeddingcurves in Lagrangian Grassmannianself-adjoint linear differential operatorsymmetric linear control systempole placement map
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 4 , 01 December 2017 , pp. 747 - 761
Copyright
Copyright © Canadian Mathematical Society 2017

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