Quasi-exactly solvable Lie superalgebras of differential operators

DOI10.1088/0305-4470/30/19/024zbMATH Open0924.17018arXivphysics/9702015OpenAlexW2052849774MaRDI QIDQ4245790

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Publication date: 9 November 1999

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Abstract: In this paper, we study Lie superalgebras of $2imes2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional superalgebras whose odd subspace is nontrivial, we find those admitting a finite-dimensional invariant module of smooth vector-valued functions, and classify all the resulting finite-dimensional modules. The latter Lie superalgebras and their modules are the building blocks in the construction of QES quantum mechanical models for spin 1/2 particles in one dimension.

Full work available at URL: https://arxiv.org/abs/physics/9702015

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