On indecomposable modules over the Virasoro algebra
classification
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modulealgebracategoryindecomposablevirasoroboundedcompositioncontains
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It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category $\cal O$, or (iii) a module in Category ${\cal O}^-$, or (iv) a module which contains the trivial module as one of its composition factors.
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