J. Kuttler, N. R. Wallach
Published 2002-11-15Version 1
It is an open problem to determine the dimension of the space of homogeneous polynomials of a fixed degree vanishing at finitely many points in the projective plane to certain multiplicities. We present various aspects of this problem and a version of a known algorithm (originally due to M. Nagata) to compute this dimension for nine or less points. Our methods are completely elementary and only involve the representation theory of SL_2.
Dissimilarity maps on trees and the representation theory of $GL_n(\C)$
The connection between representation theory and Schubert calculus
On plane Cremona transformations of fixed degree
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