Abstract
In this paper, we study the representation of an infinite-dimensional Lie algebra C related to the q-analog Virasoro-like Lie algebra. We give the necessary and sufficient conditions for the highest weight irreducible module V(ϕ) of C to be a Harish-Chandra module. We prove that the Verma C-module V¯(ϕ) is either irreducible or has the corresponding irreducible highest weight C-module V(ϕ) that is a Harish-Chandra module. We also give the maximal proper submodule of the Verma module V¯(ϕ) and the e-character of the irreducible highest weight C-module V(ϕ) when the highest weight ϕ satisfies some natural conditions. Furthermore, we give the classification of the Harish-Chandra C-modules with nontrivial central charge.
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