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

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

2010-11-14

arxiv.org/abs/1011.3267v1

Mathematics

Representation Theory

Scientific paper

Let $G$ be a complex simple Lie group and let $\g = \hbox{\rm Lie}\,G$. Let $S(\g)$ be the $G$-module of polynomial functions on $\g$ and let $\hbox{\rm Sing}\,\g$ be the closed algebraic cone of singular elements in $\g$. Let ${\cal L}\s S(\g)$ be the (graded) ideal defining $\hbox{\rm Sing}\,\g$ and let $2r$ be the dimension of a $G$-orbit of a regular element in $\g$. Then ${\cal L}^k = 0$ for any $k

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