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Register a new userNew irreducible non-weight Virasoro modules from tensor products
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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.
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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.
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 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 $n>1$ be an integer, $alphain{mathbb C}^n$, $bin{mathbb C}$, and $V$ a $mathfrak{gl}_n$-module. We define a class of weight modules $F^alpha_{b}(V)$ over $sl_{n+1}$ using the restriction of modules of tensor fields over the Lie algebra of vector fields on $n$-dimensional torus. In this paper we consider the case $n=2$ and prove the irreducibility of such 5-parameter $mathfrak{sl}_{3}$-modules $F^alpha_{b}(V)$ generically. All such modules have infinite dimensional weight spaces and lie outside of the category of Gelfand-Tsetlin modules. Hence, this construction yields new families of irreducible $mathfrak{sl}_{3}$-modules.
For an irreducible module $P$ over the Weyl algebra $mathcal{K}_n^+$ (resp. $mathcal{K}_n$) and an irreducible module $M$ over the general liner Lie algebra $mathfrak{gl}_n$, using Shens monomorphism, we make $Potimes M$ into a module over the Witt algebra $W_n^+$ (resp. over $W_n$). We obtain the necessary and sufficient conditions for $Potimes M$ to be an irreducible module over $W_n^+$ (resp. $W_n$), and determine all submodules of $Potimes M$ when it is reducible. Thus we have constructed a large family of irreducible weight modules with many different weight supports and many irreducible non-weight modules over $W_n^+$ and $W_n$.
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