On the algebraic set of singular elements in a complex simple Lie algebra

Abstract

Let G be a complex simple Lie group and let g = LieG. Let S(g) be the G-module of polynomial functions on g and let Sing g be the closed algebraic cone of singular elements in g. Let L ⊂ S(g) be the (graded) ideal defining Sing g and let 2r be the dimension of a G-orbit of a regular element in g. Then Lk = 0 for any k < r. On the other hand, there exists a… (More)

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