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Quasi exactly solvable operators and Lie superalgebras

Yves Brihaye, Betti Hartmann

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Abstract

Linear operators preserving the direct sum of polynomial rings P(m)\\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional representations of the superalgebra q(2) are recovered. Examples of Hamiltonians possessing such a hidden algebra are analyzed.

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What this paper is about

Linear operators preserving the direct sum of polynomial rings P(m)\\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional representations of the superalgebra q(2) are recovered. Examples of Hamiltonians possessing such a hidden algebra are analyzed.

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Available abstract

Linear operators preserving the direct sum of polynomial rings P(m)\\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional representations of the superalgebra q(2) are recovered. Examples of Hamiltonians possessing such a hidden algebra are analyzed.

Key concepts: Lie superalgebra, Superalgebra, Mathematics, Supermatrix, Pure mathematics, Algebra over a field, Hamiltonian (control theory), Polynomial

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