Contravariant Form on Tensor Product of Highest Weight Modules
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. Th...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210196 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Contravariant Form on Tensor Product of Highest Weight Modules / A.I. Mudrov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862699721877880832 |
|---|---|
| author | Mudrov, A.I. |
| author_facet | Mudrov, A.I. |
| citation_txt | Contravariant Form on Tensor Product of Highest Weight Modules / A.I. Mudrov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T21:24:42Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210196 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:42Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Mudrov, A.I. 2025-12-03T14:35:26Z 2019 Contravariant Form on Tensor Product of Highest Weight Modules / A.I. Mudrov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 15 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B10; 17B37 arXiv: 1709.08394 https://nasplib.isofts.kiev.ua/handle/123456789/210196 https://doi.org/10.3842/SIGMA.2019.026 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. We are grateful to Joseph Bernstein for useful discussions. We are also indebted to the anonymous referees for careful reading of the text and valuable remarks. This study was supported by the RFBR grant 15-01-03148. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Contravariant Form on Tensor Product of Highest Weight Modules Article published earlier |
| spellingShingle | Contravariant Form on Tensor Product of Highest Weight Modules Mudrov, A.I. |
| title | Contravariant Form on Tensor Product of Highest Weight Modules |
| title_full | Contravariant Form on Tensor Product of Highest Weight Modules |
| title_fullStr | Contravariant Form on Tensor Product of Highest Weight Modules |
| title_full_unstemmed | Contravariant Form on Tensor Product of Highest Weight Modules |
| title_short | Contravariant Form on Tensor Product of Highest Weight Modules |
| title_sort | contravariant form on tensor product of highest weight modules |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210196 |
| work_keys_str_mv | AT mudrovai contravariantformontensorproductofhighestweightmodules |