Casimir elements associated with Levi subalgebras of simple Lie algebras and their applications

Dmitri I. Panyushev

Let $\mathfrak{g}$ be a simple Lie algebra, $\mathfrak{h}$ a Levi subalgebra, and $C_{\mathfrak{h}}\in U(\mathfrak{h})$ the Casimir element defined via the restriction of the Killing f…