Sums of minimal orbits

Jan Draisma (Basel)

I hope to show:
  • any complex homogeneous bivariate polynomial of degree d is the sum of d terms of the form (ax+by)d, and there exist polynomials for which one really needs d such terms; and
  • any complex nxn-matrix with trace zero and an n in the upper right corner is the sum of n rank one matrices, each having trace zero and a 1 in the upper right corner;
and to explain the broader problem of which these are special cases. `Hope', for our proof of the second part is not yet quite finished. `Our': Karin Baur's and mine.

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