Representations of the Virasoro algebra. I (Q1902101)

The author first studies the structure of the tensor product of two isomorphic irreducible modules \(V_{\alpha, \beta}'\) over the Virasoro algebra case by case, and then shows that for any \(\alpha, \beta \in \mathbb{C}\), \(V_{\alpha, \beta}' \otimes V_{\alpha, \beta}' = V^+ \oplus V^-\), where \(V^+\) and \(V^-\) are indecomposable submodules, and \(\text{End}_{\text{Vir}} V^+ \cong \mathbb{C}\), \(\text{End}_{\text{Vir}}V^- \cong \mathbb{C}\), \(\text{End}_{\text{Vir}} V_{\alpha, \beta}' \otimes V_{\alpha, \beta}' \cong \mathbb{C} \oplus \mathbb{C}\).