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- W1878140754 abstract "In this paper, we use partial differential equations to find the decomposition of the polynomial algebra over the basic irreducible module of E6 into a sum of irreducible submodules. It turns out that the cubic polynomial invariant corresponding to the Dicksons' invariant trilinear form is the unique fundamental invariant. Moreover, we obtain a combinatorial identity saying that the dimensions of certain irreducible modules of E6 are correlated by the binomial coefficients of twenty-six. Furthermore, we find all the polynomial solutions for the invariant differential operator corresponding to the Dickson trilinear form in terms of the irreducible submodules." @default.
- W1878140754 created "2016-06-24" @default.
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- W1878140754 date "2008-11-10" @default.
- W1878140754 modified "2023-09-27" @default.
- W1878140754 title "Polynomial Representation of $E_7$ and Its Combinatorial and PDE Implications" @default.
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