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On algebraic classification of quasi-exactly solvable matrix models | | R. Z. Zhdanov
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17 Aug 1997 | | Journal: | J.Phys. A30 (1997) 8761-8770 | | Subject: | hep-th | | Abstract: | We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by first-order matrix differential operators. We have classified inequivalent representations of the Lie algebras of the dimension up to three by first-order matrix differential operators in one variable. Next we describe invariant finite-dimensional subspaces of the representation spaces of the one-, two-dimensional Lie algebras and of the algebra sl(2,R). These results enable constructing multi-parameter families of first- and second-order quasi-exactly solvable models. In particular, we have obtained two classes of quasi-exactly solvable matrix Schroedinger equations. | | Source: | arXiv, hep-th/9708092 | | Services: | Forum | Review | PDF | Favorites | |
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