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Register a new userIrreducible twisted Heisenberg-Virasoro modules from tensor products
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In this paper, we realize polynomial $H$-modules $Omega(lambda,alpha,beta)$ from irreducible twisted Heisenberg-Virasoro modules $A_{alpha,beta}$. It follows from $H$-modules $Omega(lambda,alpha,beta)$ and $mathrm{Ind}(M)$ that we obtain a class of natural non-weight tensor product modules $big(bigotimes_{i=1}^mOmega(lambda_i,alpha_i,beta_i)big)otimes mathrm{Ind}(M)$. Then we give the necessary and sufficient conditions under which these modules are irreducible and isomorphic, and also give that the irreducible modules in this class are new.
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In this paper, we present a class of non-weight Virasoro modules $mathcal{M}big(V,Omega(lambda_0,alpha_0)big)otimesbigotimes_{i=1}^mOmega(lambda_i,alpha_i)$ where $Omega(lambda_i,alpha_i)$ and $mathcal{M}big(V,Omega(lambda_0,alpha_0)big)$ are irreducible Virasoro modules defined in cite{LZ2} and cite{LZ} respectively. The necessary and sufficient conditions for $mathcal{M}big(V,Omega(lambda_0,alpha_0)big)otimesbigotimes_{i=1}^mOmega(lambda_i,alpha_i)$ to be irreducible are obtained. Then we determine the necessary and sufficient conditions for two such irreducible Virasoro modules to be isomorphic. At last, we show that the irreducible modules in this class are new.
In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules $Omega(lambda,alpha,h)$ defined in cite{CG}, with irreducible highest weight modules $V(theta,h)$ or with irreducible Virasoro modules Ind$_{theta}(N)$ defined in cite{MZ2}. We obtain the necessary and sufficient conditions for such tensor product modules to be irreducible, and determine the necessary and sufficient conditions for two of them to be isomorphic. These modules are not isomorphic to any other known irreducible Virasoro modules.
In this paper, we classify all indecomposable Harish-Chandra modules of the intermediate series over the twisted Heisenberg-Virasoro algebra. Meanwhile, some bosonic modules are also studied.
In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules $Omega(lambda,alpha,h)$ and $Omega(mu, b)$ with irreducible highest weight modules $V(theta,h)$ or with irreducible Virasoro modules Ind$_{theta}(N)$ defined in [MZ2]. We obtain the necessary and sufficient conditions for such tensor product modules to be irreducible, and determine the necessary and sufficient conditions for two of them to be isomorphic. We also compare these modules with other known non-weight Virasoro modules.
Let $mathfrak g(G,lambda)$ denote the deformed generalized Heisenberg-Virasoro algebra related to a complex parameter $lambda eq-1$ and an additive subgroup $G$ of $mathbb C$. For a total order on $G$ that is compatible with addition, a Verma module over $mathfrak g(G,lambda)$ is defined. In this paper, we completely determine the irreducibility of these Verma modules.
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