Unitary Harish-Chandra modules over block type Lie algebras B(q)

摘要

For any nonzero complex number q, there is a Lie algebra of Block type, denoted by B(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 B(q). Then we obtain the suficient and necessary conditions for irreducible uniformly bounded unitary Harish-Chandra modules and irreducible unitary highest (lowest) weight Harish-Chandra modules.