Quasi-exactly Solvable Lie Superalgebras of Differential Operators

Details Quasi-exactly Solvable Lie Superalgebras of Differential Operators Quasi-exactly Solvable Lie Superalgebras of Differential Operators

1997-02-17

arxiv.org/abs/physics/9702015v1

J.Phys.A30:6879-6892,1997

Physics

Mathematical Physics

LaTeX2e using the amstex and amssymb packages, 24 pages

Scientific paper

10.1088/0305-4470/30/19/024

In this paper, we study Lie superalgebras of $2\times 2$ 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.

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