
Journal of Lie Theory 23 (2013), No. 3, 827836 Copyright Heldermann Verlag 2013 Unitary HarishChandra 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 HarishChandra modules for these algebras. We first give a description of conjugatelinear antiinvolutions on q. Then we obtain the sufficient and necessary conditions for irreducible uniformly bounded unitary HarishChandra modules and irreducible unitary highest (lowest) weight HarishChandra modules. Keywords: Block type algebra, Virasoro algebra, HarishChandra module, intermediate series module. MSC: 17B10, 17B20, 17B65, 17B66, 17B68 [ Fulltextpdf (288 KB)] for subscribers only. 