Abstract
We find expressions of the polynomials defining the dual varieties of Grassmannians Gr(3,9) and Gr(4,8) both in terms of the fundamental invariants and in terms of a generic semi-simple element. We restrict the polynomial defining the dual of the adjoint orbit of E8 and obtain the polynomials of interest as factors. To find an expression of the Gr(4,8) discriminant in terms of fundamental invariants, which has 15,942 terms, we perform interpolation with mod-p reductions and rational reconstruction. From these expressions for the discriminants of Gr(3,9) and Gr(4,8) we also obtain expressions for well-known hyperdeterminants of formats 3×3×3 and 2×2×2×2.
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