Generalized polynomial modules over the Virasoro algebra

Liu, Genqiang; Zhao, Yueqiang

doi:10.1090/proc/13171

Generalized polynomial modules over the Virasoro algebra
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by Genqiang Liu and Yueqiang Zhao PDF

Proc. Amer. Math. Soc. 144 (2016), 5103-5112 Request permission

Abstract:

Let $\mathcal {B}_r$ be the $(r+1)$-dimensional quotient Lie algebra of the positive part of the Virasoro algebra $\mathcal {V}$. Irreducible $\mathcal {B}_r$-modules were used to construct irreducible Whittaker modules in a work of Mazorchuk and Zhao (2014) and irreducible weight modules with infinite dimensional weight spaces over $\mathcal {V}$ in a work of Liu, Lu and Zhao (2015). In the present paper, we construct non-weight Virasoro modules $F(M, \Omega (\lambda ,\beta ))$ from irreducible $\mathcal {B}_r$-modules $M$ and $(\mathcal {A},\mathcal {V})$-modules $\Omega (\lambda ,\beta )$. We give necessary and sufficient conditions for the Virasoro module $F(M, \Omega (\lambda ,\beta ))$ to be irreducible. Using the weighting functor introduced by J. Nilsson, we also determine necessary and sufficient conditions for two $F(M, \Omega (\lambda ,\beta ))$ to be isomorphic.

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