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Showing 1 to 2 of 2 for “"graded Lie algebras"”.
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Graded Lie Algebras, Compactified Jacobians and Arithmetic Statistics
A simply laced Dynkin diagram gives rise to a family of curves over Q and a coregular representation, using deformations of simple singularities and Vinberg theory respectively. Thorne has conjectured and partially proven a strong link between the arithmetic of these curves and the rational orbits …
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Arithmetic statistics and Vinberg representations
… polynomials arising from the invariant theory of Lie algebras. The proof of our result follows the same steps as Bhargava--Shankar--Wang's proof, reinterpreted in further generality within the general context of Vinberg theory. We adapt their $Q$-invariant method to turn mod $p^2$ sieves into mod …