Hitchin's Conjecture for $\mathfrak{sl}_n$ in Odd Prime Degree

We prove Hitchin's conjecture for $\mathfrak{sl}_n$ in every odd prime degree. More precisely, let $p=2k+1$ be prime and let $n\geq k+1$. Every nonzero primitive element $α\inΛ^p(\mathfrak{sl}_n^*)^{\mathfrak{sl}_n}$ is nonzero on the top exterior power of the unique $p$-dimensional irreducible subm