A classification of lowest weight irreducible modules over ${\mathbb{Z}}_2^2$-graded extension of $osp(1|2)$

Abstract

We investigate representations of the ${\mathbb{Z}}_2^2$-graded extension of $osp(1|2)$ which is the spectrum generating algebra of the recently introduced ${\mathbb{Z}}_2^2$-graded version of superconformal mechanics. The main result is a classification of irreducible lowest weight modules of the ${\mathbb{Z}}_2^2$-graded extension of $osp(1|2)$. This is done via introduction of Verma modules and its maximal invariant submodule generated by singular vectors. Explicit formula of all singular vectors are also presented.

arXiv comment26pages, no figure

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Cited by in corpus (8)

• Comments of ${\mathbb{Z}}_2^2$-supersymmetry in superfield formalism
• Irreducible representations of ${\mathbb{Z}}_2^2$-graded $\mathcal{N}=2$ supersymmetry algebra and ${\mathbb{Z}}_2^2$-graded supermechanics
• New aspects of the Z${}_{\text{2}}$ $\times$ Z${}_{\text{2}}$-graded 1D superspace: induced strings and 2D relativistic models
• Integrable ${\mathbb{Z}}_2^2$-graded Extensions of the Liouville and Sinh-Gordon Theories
• ${\mathbb{Z}}_2^2$-graded supersymmetry via superfield on minimal ${\mathbb{Z}}_2^2$-superspace
• $\mathcal{N}=2$ Double graded supersymmetric quantum mechanics via dimensional reduction
• Affine extensions of ${\mathbb{Z}}_2^2$-graded $osp(1|2)$ and Virasoro algebra
• An integrable hierarchy associated with loop extension of ${\mathbb{Z}}_2^2$-graded $\mathfrak{osp}(1|2)$