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Quantum deformations of generalized Kac-Moody algebras and their modules

Cited 58 time in Web of Science Cited 51 time in Scopus
Authors
Kang, Seok-Jin
Issue Date
1995
Publisher
Elsevier
Citation
J. Algebra 175 (1995), 1041-1066
Abstract
We construct quantum groups U_q(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 sho that, for generic q, Verma modules over U(g) with integral highest weights and irreducible highest weight modules over U(g) with dominant integral highests can be deformed to those over U_q(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 U_q(g) with dominant integral highest weights are given by the Weyl-Kac-Borcherds formula.
ISSN
0021-8693
Language
English
URI
https://hdl.handle.net/10371/12190
DOI
https://doi.org/10.1006/jabr.1995.1226
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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