2381/44772 Andrey I. Mudrov Andrey I. Mudrov Contravariant form on tensor product of highest weight modules University of Leicester 2019 highest weight modules contravariant form tensor product complete reducibility 2019-07-09 14:25:21 Journal contribution https://figshare.le.ac.uk/articles/journal_contribution/Contravariant_form_on_tensor_product_of_highest_weight_modules/10203698 We give a criterion for complete reducibility of tensor product V ⊗ Z of two irreducible highest weight modules V and Z over a classical or quantum semi-simple group in terms of a contravariant symmetric bilinear form on V ⊗ Z. This form is the product of the canonical contravariant forms on V and Z. Then V ⊗ Z is completely reducible if and only if the form is non-degenerate when restricted to the sum of all highest weight submodules in V ⊗ Z or equivalently to the span of singular vectors.