Journal of Lie Theory 23 (2013), No. 1, 159--176
Copyright Heldermann Verlag 2013
Unitary Highest Weight Modules over Block Type Lie Algebras B(q)
Chunguang Xia
Wu Wen-Tsun 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
[Abstract-pdf]
\def\BB{{\cal B}(q)} We classify the unitary quasifinite irreducible highest weight modules over the Block type Lie algebras $\BB$ for all non-zero 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
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