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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2019 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2019
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210196 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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.
|
|---|---|
| ISSN: | 1815-0659 |