sigma19-026.pdf (350.87 kB)
Download file

Contravariant form on tensor product of highest weight modules

Download (350.87 kB)
journal contribution
posted on 09.07.2019, 14:25 by Andrey I. Mudrov
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.

Funding

This study was supported by the RFBR grant 15-01-031

History

Citation

Symmetry, Integrability and Geometry : Methods and Applications, 2019, 15 (026), pp. ?-? (10)

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

VoR (Version of Record)

Published in

Symmetry

Publisher

National Academy of Science of Ukraine

issn

1815-0659

Acceptance date

25/03/2019

Copyright date

2019

Available date

09/07/2019

Publisher version

https://www.emis.de/journals/SIGMA/2019/026/

Notes

2010 Mathematics Subject Classification: 17B10; 17B37

Language

en