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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

Xiangqian Guo
Department of Mathematics, Zhengzhou University, Zhengzhou 450001, Henan, P. R. China

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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