Journal of Lie Theory 23 (2013), No. 3, 827--836
Copyright Heldermann Verlag 2013
Unitary Harish-Chandra Modules over Block Type Lie Algebras B(q)
Hongjia Chen
School of Mathematical Sciences, University of Science and Technology, Hefei 230026, Anhui, P. R. China
hjchenmath@gmail.com
Xiangqian Guo
Department of Mathematics, Zhengzhou University, Zhengzhou 450001, Henan, P. R. China
guoxq@amss.ac.cn
For any nonzero complex number q, there is a Lie algebra of Block type, denoted by q. In this paper, we classify the unitary Harish-Chandra modules for these algebras. We first give a description of conjugate-linear anti-involutions on q. Then we obtain the sufficient and necessary conditions for irreducible uniformly bounded unitary Harish-Chandra modules and irreducible unitary highest (lowest) weight Harish-Chandra modules.
Keywords: Block type algebra, Virasoro algebra, Harish-Chandra module, intermediate series module.
MSC: 17B10, 17B20, 17B65, 17B66, 17B68
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