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Contravariant forms and extremal projectors |
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| Institution: | 1. Department of Mathematics, University of California, Riverside, Riverside, CA 92521, United States of America;2. Beijing Advanced Innovation Center for Imaging Theory and Technology, Beijing 100048, China;3. Capital Normal University, Academy for Multidisciplinary Studies, Beijing 100048, China |
| Abstract: | Tensor product of irreducible modules of highest weight over a semi-simple quantum group is completely reducible if and only if a natural contravariant form is non-degenerate when restricted to the span of singular vectors. We express this restriction through the extremal projector of the quantum group providing a computationally feasible criterion for complete reducibility of tensor products. |
| Keywords: | Highest weight modules Tensor product Complete reducibility Contravariant form Extremal projector |
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