Representations of the Virasoro Algebra, I

Abstract

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 ∈ C, V′α,β ⊗ V′α,β = V+ ⊕ V-, where V+ and V- are indecomposable submodules. And EndVirV+ ≅ C, EndVirV- ≅ C, EndVirV′α,β ⊗ V′α,β ≅ C ⊕ C. Further some of the subquotients of V+ and V- are studied. © 1995 Academic Press, Inc.