The exceptional Lie algebra G2 and binary cubics M.J. Slupinski Let P
The exceptional Lie algebra G2 and binary cubics. M.J. Slupinski. Let P(x, y) be a binary cubic, i.e., a homogeneous polynomial of degree three in two variables.
The exceptional Lie algebra G2 and binary cubics M.J. Slupinski Let P (x, y) be a binary cubic, i.e., a homogeneous polynomial of degree three in two variables. To P (x, y) one can naturally associate a scalar DP (the discriminant), a binary quadratic form qP (x, y) and another binary cubic GP (x, y). In 1844 G. Eisenstein proved the relation 4qP (x, y)3 = GP (x, y)2 − DP P (x, y)2 . In the talk I will give a purely symplectic formulation of this relation and show that it is a special case of a more general relation satisfied by the symplectic covariants of a symplectic module which one can associate to any simple Lie algebra. From this point of view, the classical Eisenstein relation comes from the exceptionial Lie algebra G2 . This is joint work with R. J. Stanton.
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