Tensor product realizations of simple torsion free modules (Q2715669)

The authors realize simple torsion-free (\(=\) dense \(=\) cuspidal) \(sl(n,{\mathbb C})\)-modules with finite-dimensional weight spaces, recently classified by \textit{O. Mathieu} [Ann. Inst. Fourier 50, No. 2, 537-592 (2000; Zbl 0962.17002)], as certain submodules of the easily constructed tensor product modules. In the \(sl(n,{\mathbb C})\) case this proves the conjecture, formulated by the second author in [Infinite dimensional Lie modules. Queen's Pap. Pure Appl. Math. 94, 67-72 (1994; Zbl 0818.17025)]. It is also said that in the case of symplectic Lie algebra (the only one left for which simple torsion-free modules with finite-dimensional weight spaces exist) the conjecture follows directly from Mathieu's results.