Injectivity of Generalized Wronski Maps
Printed: Dec 2017
We study linear projections on Plücker space whose restriction
to the Grassmannian is a non-trivial branched
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 differential operator
and pole placement map for
symmetric linear systems are natural examples.
Wronski map, Plücker embedding, curves in Lagrangian Grassmannian, self-adjoint linear differential operator, symmetric linear control system, pole placement map
14M15 - Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
34A30 - Linear equations and systems, general
93B55 - Pole and zero placement problems