Representations of SL₂ and the distribution of points in Pⁿ
Kuttler, J. · Wallach, N. R.
الأصل · EN
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 SL₂.
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