Abstract
In this article, we study Whittaker modules over generalized Virasoro algebras relative to some total order. We give the description of any Whittaker module and its Whittaker vectors. In particular, we determine all simple Whittaker modules, which provide the first known examples of simple nonweight modules over generalized Virasoro algebras. On the other hand, we also show that any Whittaker module over any generalized Virasoro algebra can be induced from a Whittaker module over some Virasoro subalgebra.
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