On \(sl(n)\)-modules of finite-dimensional weight (Q1316825)

The author describes a set of representations of \(sl(n)\) on certain subspaces of the infinite-dimensional complex space with the canonical basis \(\alpha(m)\) where \(m\) runs over all elements of the lattice \(\mathbb{Z}^{n(n-1)/2}\). It is then stated that for any indecomposable scalar representation \(\rho\) of \(sl(n)\) (\(n\neq 3\)) of finite-dimensional weight and any \(\nu\in {\mathfrak h}^*\) (\({\mathfrak h}\) the Cartan subalgebra consisting of diagonal matrices in \(sl(n)\)) there exists a representation \(\tau\) in this set such that \(\rho\) and \(\tau\) are isomorphic in the weight \(\nu\).