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Register a new userVerma modules over deformed generalized Heisenberg-Virasoro algebras
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Chengkang Xu
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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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Let $mathbb{F}$ be a field of characteristic 0, $G$ an additive subgroup of $mathbb{F}$, $alphain mathbb{F}$ satisfying $alpha otin G, 2alphain G$. We define a class of infinite-dimensional Lie algebras which are called generalized Schr{o}dinger-Virasoro algebras and use $mathfrak{gsv}[G,alpha]$ to denote the one corresponding to $G$ and $alpha$. In this paper the automorphism group and irreducibility of Verma modules for $mathfrak{gsv}[G,alpha]$ are completely determined.
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