Abstract:
Let $\mathfrak g$ be a simple Lie algebra with Cartan subalgebra $\mathfrak{h}$ and Weyl
group $W$. We build up a graded isomorphism $\smash{\bigl(\bigwedge\mathfrak{h}\otimes\mathcal
H\otimes \mathfrak{h}\big)\vphantom)^W}\to \bigl(\bigwedge \mathfrak{g}\otimes \mathfrak{g}\big)^\mathfrak{g}$ of $\bigl(\bigwedge
\mathfrak{g}\big)^\mathfrak{g}\cong S(\mathfrak{h})^W$-modules, where $\mathcal H$ is the space
of $W$-harmonics. In this way we prove an enhanced form of a conjecture of
Reeder for the adjoint representation.
Key words and phrases:exterior algebra, covariants, small representation, Dunkl operators.
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