Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 107, 24 pages      arXiv:0902.1106      https://doi.org/10.3842/SIGMA.2009.107

On Projective Equivalence of Univariate Polynomial Subspaces

Peter Crooks a and Robert Milson b
a) Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4
b) Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5

Received June 05, 2009, in final form December 03, 2009; Published online December 06, 2009

Abstract
We pose and solve the equivalence problem for subspaces of Pn, the (n+1) dimensional vector space of univariate polynomials of degree ≤ n. The group of interest is SL2 acting by projective transformations on the Grassmannian variety GkPn of k-dimensional subspaces. We establish the equivariance of the Wronski map and use this map to reduce the subspace equivalence problem to the equivalence problem for binary forms.

Key words: polynomial subspaces; projective equivalence.

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