
Journal of Lie Theory 23 (2013), No. 1, 159176 Copyright Heldermann Verlag 2013 Unitary Highest Weight Modules over Block Type Lie Algebras B(q) Chunguang Xia Wu WenTsun Key Laboratory of Mathematics, University of Science and Technology, Hefei 230026, P. R. of China and: School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia chgxia@mail.ustc.edu.cn Ruibin Zhang School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia ruibin.zhang@sydney.edu.au [Abstractpdf] \def\BB{{\cal B}(q)} We classify the unitary quasifinite irreducible highest weight modules over the Block type Lie algebras $\BB$ for all nonzero values of the parameter $q$. The algebra $\BB$ contains the Virasoro algebra as a subalgebra and thus is likely to have applications in conformal field theory. Keywords: Block type Lie algebras, quasifinite highest weight modules, unitarity. MSC: 17B10, 17B65, 17B68, 81R10 [ Fulltextpdf (312 KB)] for subscribers only. 