## An Example Using Chevalley Restriction

Here is a classic problem of geometric invariant theory: let $ G$ be a reductive linear algebraic group such as $ \mathrm{GL}_n$ and let $ \mathfrak{g}$ be its Lie algebra. Determine the invariant functions $ k[\mathfrak{g}]^G$, where $ G$ acts on $ \mathfrak{g}$ via the adjoint action. This problem is motivated by the search for […]