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Contravariant form on tensor product of highest weight modules
journal contribution
posted on 2019-07-09, 14:25 authored by Andrey I. MudrovWe 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.
Funding
This study was supported by the RFBR grant 15-01-031
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Citation
Symmetry, Integrability and Geometry : Methods and Applications, 2019, 15 (026), pp. ?-? (10)Author affiliation
/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of MathematicsVersion
- VoR (Version of Record)
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SymmetryPublisher
National Academy of Science of Ukraineissn
1815-0659Acceptance date
2019-03-25Copyright date
2019Available date
2019-07-09Publisher DOI
Publisher version
https://www.emis.de/journals/SIGMA/2019/026/Notes
2010 Mathematics Subject Classification: 17B10; 17B37Language
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