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Register a new userHarish-Chandra Modules Over the Twisted Heisenberg-Virasoro Algebra
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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.
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In this paper, the conjugate-linear anti-involutions and the unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra are classified respectively. We prove that any unitary irreducible module of the intermediate series over the twisted Heisenberg-Virasoro algebra is of the form $mathcal{A}_{a,b,c}$ for $ain mathbb{R}, bin 1/2+sqrt{-1}mathbb{R}, cin mathbb{C}.$
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.
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.
Mathematical physicists have studied degenerations of Lie groups and their representations, which they call contractions. In this paper we study these contractions, and also other families, within the framework of algebraic families of Harish-Chandra modules. We construct a family that incorporates both a real reductive group and its compact form, separate parts of which have been studied individually as contractions. We give a complete classification of generically irreducible families of Harish-Chandra modules in the case of the family associated to SL(2, R).
We give conditions for unitarizability of Harish-Chandra super modules for Lie supergroups and superalgebras.
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