On Projective Equivalence of Univariate Polynomial Subspaces

Abstract

We pose and solve the equivalence problem for subspaces of ${\mathcal{P}}_n$, the $(n+1)$ dimensional vector space of univariate polynomials of degree $\le n$. The group of interest is ${\mathrm{SL}}_2$ acting by projective transformations on the Grassmannian variety ${\mathcal{G}}_k{\mathcal{P}}_n$ 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.

References in corpus (3)

• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
• An Extension of Bochner's Problem: Exceptional Invariant Subspaces
• A theorem of Heine-Stieltjes, the Wronski map, and Bethe vectors in the sl_p Gaudin model