Infinite-dimensional simple U(h)-finite modules are U(h)-torsion free, and the new category A^irr of such modules is classified for type C and partially for type A.
Lie Groups and Lie Algebras: Chapters 7-9 (Elements of Mathe matics)
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$\mathcal{U}(\mathfrak{h})$-finite modules and weight modules I: weighting functors, almost-coherent families and category $\mathfrak{A}^{\text{irr}}$
Infinite-dimensional simple U(h)-finite modules are U(h)-torsion free, and the new category A^irr of such modules is classified for type C and partially for type A.