Journal of Lie Theory

no. 3
Unitary Harish-Chandra Modules over Block Type Lie Algebras B(q)
Journal of Lie Theory, Volume 23 (2013) no. 3, pp. 827-836
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.
DOI: 10.5802/jolt.752
Classification: 17B10, 17B20, 17B65, 17B66, 17B68
Keywords: Block type algebra, Virasoro algebra, Harish-Chandra module, intermediate series module 
@article{JOLT_2013_23_3_a12,
     author = {H. Chen and X. Guo},
     title = {Unitary {Harish-Chandra} {Modules} over {Block} {Type} {Lie} {Algebras} {B(q)}},
     journal = {Journal of Lie Theory},
     pages = {827--836},
     year = {2013},
     volume = {23},
     number = {3},
     doi = {10.5802/jolt.752},
     zbl = {1287.17014},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.752/}
}
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%A X. Guo
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H. Chen; X. Guo. Unitary Harish-Chandra Modules over Block Type Lie Algebras B(q). Journal of Lie Theory, Volume 23 (2013) no. 3, pp. 827-836. doi: 10.5802/jolt.752

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