Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra
Abstract
In this paper, we provide a uniform method to thoroughly classify all Harish-Chandra modules over some Lie algebras related to the Virasoro algebras. We first classify such modules over the Lie algebra W()[s] for s=0,12. With this result and method, we can also do such works for some Lie algebras and superconformal algebras related to the Virasoro algebra, including the several kinds of Schr\"odinger-Virasoro Lie algebras, which are open up to now.
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