Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal algebra

In this paper, we classify all finite irreducible conformal modules over a class of Lie conformal algebrasW(b)with b ε C related to theVirasoro conformal algebra.Explicitly, any finite irreducible conformal module overW(b) is proved to be isomorphic to M_δ,α,β with δ ≠ 0 or β ≠ 0 if b = 0, or M_δ,α with δ ≠ 0 if b ≠ 0. As a byproduct, all finite irreducible conformal modules over the Heisenberg-Virasoro conformal alge- bra and the W(2, 2) Lie conformal algebra are classified. Finally, the same thing is done for the Schrödinger-Virasoro conformal algebra.