Abstract
Let g be a finite dimensional complex simple Lie algebra and ĝ the associated affine Lie algebra. Let V be a finite dimensional irreducible g-module and X an integrable highest weight ĝ-module. We show that the tensor product of X with the space L( V) of loops in V is reducible if the highest weight of X is “large” compared with that of V. (This complements the result of a previous paper in which we showed that the tensor product is irreducible if the highest weight of X is “small” compared with that of V.) The proof makes use of a Lie superalgebra constructed from ĝ and V.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
