On Projective Equivalence of Univariate Polynomial Subspaces

Details On Projective Equivalence of Univariate Polynomial Subspaces On Projective Equivalence of Univariate Polynomial Subspaces

2009-02-06

arxiv.org/abs/0902.1106v7

SIGMA 5 (2009), 107, 24 pages

Mathematics

Quantum Algebra

Scientific paper

10.3842/SIGMA.2009.107

We pose and solve the equivalence problem for subspaces of ${\mathcal P}_n$, the $(n+1)$ dimensional vector space of univariate polynomials of degree $\leq n$. The group of interest is ${\rm SL}_2$ 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.

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