Injectivity of Generalized Wronski Maps. Issue 4 (1st December 2017)

• Record Type: Journal Article
• Authors: Huang, Yanhe; Sottile, Frank; Zelenko, Igor
• Is Part Of: Canadian mathematical bulletin =. Volume 60:Issue 4(2017)
• Page Start: 747
• Page End: 761
• Publication Date: 2017-12-01
• Subjects: 14M15 -- 34A30 -- 93B55; Wronski map -- Plücker embedding -- curves in Lagrangian Grassmannian -- self-adjoint linear differential operator -- symmetric linear control system -- pole placement map; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2017-001-0
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: 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.