Representations of the Virasoro Algebra, I Original Research Article

In the present paper, the structure of the tenser product of two isomorphic irreducible modules V′α,β over the Virasoro algebra is studied case by case. The following results are proved: For any α, β set membership, variant C, V′α,β circle times operator V′α,β = V+ circled plus V−, where V+ and V− are indecomposable submodules. And EndVirV+ congruent with C, EndVirV− congruent with C, EndVirV′α,β circle times operator V′α,β congruent with C circled plus C. Further some of the subquotients of V+ and V− are studied.