Abstract
We construct quantum groups Uq(g) associated with generalized Kac-Moody algebras g with admissible Borcherds-Cartan matrices. We also construct quantum deformations of highest weight modules over U(g) with integral highest weights. We show that, for generic q, Verma modules over U(g) with integral highest weights and irreducible highest weight modules over U(g) with dominant integral highest weights can be deformed to those over Uq(g) in such a way that the dimensions of weight spaces are invariant under the deformation. In particular, for generic q, the characters of irreducible highest weight modules over Uq(g) with dominant integral highest weights are given by the Weyl-Kac-Borcherds formula.
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.
