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.

26pages, no figure

References in corpus (3)

• Once more on parastatistics
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded Lie Symmetries of the Lévy-Leblond Equations
• Riemannian structures on ${\mathbb{Z}}_2^n$-manifolds

Cited by in corpus (2)

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